This is a work-in-progress article that will highlight strange outliers in the fabric of spacetime in the Mushroom Kingdom. Because if there's any universe that can make golf interesting, it's this one. I will explore and attempt to explain with text and/or video various anomalies that you should watch out for and either avoid or exploit them. These things include: Cup Warp Glitch, non-solid Ground, random slope ramps/glitches, the High Slice mishit trick, dunks, and more!

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CUP WARP GLITCH: This is a phenomenon that has until recently been unexplored and unexploited. It is not advised to attempt this trick in an RTA run, but it makes for great entertainment for LOLs or potentially for a tool-assisted superplay. I could try to explain this freak of nature, but I think some video embeds would do far more justice:

(Starts at 0:56)

I think what is happening here is that the cup itself extends vertically to the bottom edge of OB on the map. When the ball lands anywhere in this zone, the game assumes that the ball is going toward the cup itself and thus repositions the ball at the top and the ball continues at the velocity is was going up to the aforementioned zone. Your aim and distance control have to be virtually perfect in order for the ball to stay inside the cup once it is warped. If the ball has too much velocity and is too low, the ball will pop out of the cup and continue along the Green. If you are successful, there will be an unusual camera angle and the ball will stop in the cup as if you had directly dunked the ball inside on the fly. This is only possible (to my knowledge) on cups/Greens that are suspended above non-solid spaces, as opposed to rock or solid ground. If the ball can't reach the zone directly beneath the cup, then there's no warp to be had. This trick is possible on Bowser Badlands 9 (the front-most cup), Badlands 11, Badlands 17, and most of Congo Canopy (2, 3, 6, 8, 9, 10, 11, 13, 14, 16, & 18 should all work with perfect shots).

This trick also works for the PAL version of the game, as confirmed by MattTheMan2708. Notice the unusual camera angles.

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BIG BOUNCE: This technique exploits the physics of the Fast Fairway and Backspin to create shots that bounce much higher and farther than what the Simulation Line would have you believe. If you remember your elementary physics, you'll know that Backspin placed on a ball creates an upward force in a phenomenon known as the Magnus effect. The combination of forward velocity and backward rotation allows for higher bounces. This is magnified by the Fast Fairway to the point where you can add 20+ yards to the length of a bounce and 5+ yards in height, which is enough to cross gaps and even land in Pipes. While this can be unintentionally exploited on holes throughout Blooper Bay to hop over bunkers, this can be harnessed for the creation of strats you never thought possible.

Examples:

Reaching the Green Pipe on Peach's Castle Grounds 1 with weaker characters:

Reaching the final island on Peach's Castle Grounds 4 off a big bounce:

Skipping over the chasm on the right side of Blooper Bay 13 (in case you want a better angle to the Green): VIDEO COMING SOON!

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DUNKS: This is a technique in which you can instantly hole-out by landing the ball directly in the cup without roll. All you have to do is place the Landing Point directly on the cup (even the slightest off and you'll Pin-Shot instead). Hit your marks exactly and hope you get 0% RNG (for -1%, if you think you'll get a Pin Shot, use no Spin. Otherwise, consider Backspin or Super Backspin). If there is any wind, your chances are minimal of pulling this off, though you may be able to dunk an Approach shot with minimal wind and some adjustment. Consider whether the extra stroke and time saved would be worth the time spent adjusting and the consequences of failure. It may prove to be the difference that allows you to skip a (longer) hole, so keep this in mind.

Here are some dunks used as Ace Strats for Star Petey Piranha at Lakitu Valley for Lakitu Cup and the Character Matches against Koopa Troopa and Peach (since there is no Wind):

Hole 3 (139y Flag):

Hole 12 (157y Flag and 166y Rain Flag):

I was lucky enough to witness this live on Twitch. Here's an awesome Clip (Shoutouts to RedFalconGames)!
(Starts at 3:00).

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HIGH SLICE TRICK: This isn't so much a glitch as much as a trick that can be used to save strokes on short but high and compact holes like Peach's Castle Grounds 8 or Bowser Badlands 1. By intentionally mishitting the sweet spot timing far too early, you get a shot that loses significant distance, curves greatly to the right for Right-handed golfers (or left for Lefties, which you need for Badlands 1), and attains significant height. If you mishit only enough to barely make your mark within the Impact Zone timing (the red bar at the bottom), then you'll still get a significant curve and loft increase without destroying the power of the shot too badly. This clip demonstrates the technique for a couple of holes:

This clip is taken from the Star Shadow Mario vs Ace Petey Piranha match. It took a minute to figure this shot out, but boy did it pay off! I managed to save Birdie to even the hole and then ¤SPOILERS¤. Go watch the full video at your leisure. It's among my proudest achievements.

FULL VIDEO:

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NON-SOLID GROUND: There are some tiny and specific areas in the game where the ground isn't correctly rendered and the ball will go right through it. So far, this is confirmed for Bowser Badlands 7 & Peach's Castle Grounds 18. In both cases, the ball is drastically overhit. I can only wonder why this would happen.

Here's my clip from Badlands 7:

Here's a clip by WhiteKhakis from Peach's Castle Grounds 18:

Here's a clip by Bluekandy from Blooper Bay 7:

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RANDOM SLOPE ANOMALIES: Much like the previously aforementioned non-solid ground glitch, these are specific areas that aren't quite rendered correctly, so the ball behaves erratically and not how you would expect it too. Thus, it is prudent to try to avoid these spots. The front-left side of the Fringe in Lakitu 2 has a strange invisible bump that will send your ball flying, so try to aim a bit more right. The front Fringe of Blooper Bay 1 is abnormally good at stopping balls to the point that a 4-iron will bounce BACK even without Backspin and miss the Green, so it is best to either land the ball just short or just beyond the Fringe of this Green or use Topspin, depending on where the Pin is.

Here's an old highlight from DustyNumbers I dug up that demonstrates the glitched contour of the Fringe in LV 2.

In addition, you will sometimes have the ball hop during a putt on the Green. While this may seem cheap, it is analogous to real life, where a brisk putt on a slightly imperfect surface would cause some skipping, especially with an imperfect putting stroke. Usually, when this happens, you'd probably miss the cup anyway because you're hitting the ball too hard.

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BUNKER/RAMP PUTTING: This is a trick to get yourself out of steep holes, such as pot bunkers in Blooper Bay, with some degree of efficiency. With any luck, depending on your Lie, you can get quite a bit of distance out of a bunker or against a rock because the surface will act as a ramp to catch your hard and fast zero-lofted putting stroke. This trick may also salvage the hole if you mishit the Green on holes such as Blooper Bay 2 or 7, or if you get stuck directly against steep rocks such as Blooper Bay 18, Badlands 3 or 5. Distance control is quite difficult, but 60 feet will probably barely get you out, while 80-100 will get you a fair bit of extra distance. A full 320-foot putt out of a deep Fairway bunker might send you 80+ yards, which looks cool and might save your bacon, albeit sans a Birdie opportunity. Be sure to practice this technique, because it could be the difference between epic win and epic fail.

Credits to UniversalGiant for this accidental gem! One mark harder and it was probably in.

This is an excellent example of the ramp putting effect put to use to accidental save the hole.

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BACKSPIN ABUSE: If you're looking to have some fun breaking physics, get yourself a character with a high Spin stat (Mario, Bowser, or a customized Neil/Ella), the Super Spin clubs (trade the Custom Ticket D in Mario Golf: Advance Tour to the Clubmaker, then link the game to Toadstool Tour), and go into Training Mode. Set the wind to be a strong headwind, play your highest shot against the wind, and see what happens when you land in certain areas or bounce off of rocks. Weird stuff happens. Here are some examples:

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NEGATIVE-SCORE MULLIGAN GLITCH: I personally haven't explored this glitch. Apparently, if you play a specific shot on a hole where a Thwomp can bury your ball (6, 10, 14 or 17), and use Mulligans, your score will DECREASE and go into negative strokes. Unfortunately, there are no Mulligans in Tournaments, so I don't think this can be exploited for speedruns (the extra time to go through the dialogue box every shot would annihilate any time-saves anyway, even if it allowed you skip another hole). Here is a video anyway:

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I DON'T EVEN! MUSHROOM SOFTLOCK: This clip comes from a (failed?) speedrun attempt by Likeanoob100. Upon mishitting a shot from in front of a mushroom, the ball launched indefinitely toward the heavens, nowhere to be seen. The distance escalates rapidly, until 512 MILES LATER, the game softlocks. If ANYBODY HAS ANY IDEA WHAT ON EARTH HAPPENED, LET ME KNOW. Here is the clip (1:12 in):

Edit (Spyfox): Additional Mushroom Anomalies Have Been Unearthed!! If somehow you are able to perform the shot listed above and ESCAPE before reaching terminal velocity, some crazy physics may occur which can put an absolutely insane amount of spin on the ball. Still doesn't confirm why the hell this happens.. but it is easier to see the interaction between the ball and the 2 mushrooms when the frames don't immediately take a dump.

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I DON'T EVEN! AT ALL! THERE IS NO SAFE SHOT ANYMORE! This clip seems to combine the Cup Warp Glitch and the Non-Solid Ground glitch in one f¤¤k-you nutshot. What looked like an excellent dunk instantly turned OB. I slowed it down, magnified, enhanced, and analyzed, but I'm at a loss. You tell me what you think happened here.

Another example, a seemingly innocuous dunk by MichaelT00:

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LAVA/MUSHROOM GLITCHES This is another one of those things that can only be found by a brutally freak accident. If the ball lands perfectly in lava surrounded by rock, the ball can behave very strangely. It is possible to land in a pocket within lava that the game counts as a Water Hazard. Cue obligatory examples:

Another streamer, Guzzinator484, took this to a new dimension by accidentally finding a way to land in lava and stop SUSPENDED on the nearby sheer cliff face. I still don't know how this works.

While experimenting to replicate this phenomenon, I discovered that the game is capable of freezing outright for quite a long time, the while calculating a convoluted landing point for the ball - IN MIDAIR!

Yet another streamer, StylishYoshi, discovered a way to do this outside of Training Mode. Because this is outside of Training Mode, there are no extra freezes while aiming and just before making the shot. The game isn't trying to calculate the roll to create the Stopping Point; instead you are merely shown the Landing Point. This makes this whole thing a freak accident. Since there are so many freezes, this has to be shown in parts.