Throughout the game, there are a number of softlocks which can trigger by trying to play as fast as possible.

Black Flag - Container

In the first mission, the last target is a container on the docks which triggers an explosion and the end of the mission. Intuitively, the way fastest to destroy this is to be firing at it before it becomes destructible, causing it to be destroyed as soon as it spawns. However, if it is destroyed as soon as it spawns it won’t trigger the explosion nor the end of the mission, leaving you flying around infinitely until you quit.

To avoid this simply give it a little time before destroying it, what works is to start firing your guns as soon as its marker appears, in the small amount of time taken for your bullets to hit it, the softlock window will have passed, even if fired at close range.

Presidia - Naval Targets

In mission 20 when the Naval segment starts a number of ships in the port section of the city will become active and marked as priority targets, with all ships having to be sunk to progress to the final phase of the mission. However, destroying any priority targets (the hulls of the ships, destroying any of the weaponry on the ships is fine) before a certain part in the dialogue will cause the mission to softlock and not progress after the naval targets are all sunk. Waiting for AWACS Galaxy to say “Hitman Team” in the dialogue, “Eminent Domain reports last remaining naval forces are pushing out to meet her. Hitman Team provide support.” before sinking a ship will avoid this softlock.

Bossfights

For this, bossfights are defined as when enemies spawn and have an introduction overlay, after which health bars are displayed at the bottom of the screen. These bossfights are all believed to be softlock risks as three have known softlocks all caused by dealing too much damage before the intro overlay is finished. For most bossfights there is very little delay between the spawn and the overlay so the window for softlocking is fairly short, however for those with lengthy intro dialogue or sequences, care should be taken to avoid finishing the fight before it has ‘started’.

Midnight Light - SP43R Takeoff

As the bossfight starts at the end of mission 12, SP34R will spawn and take off from the platform's runway during which it can be damaged, however dealing enough damage to deplete the first health bar and put SP34R into phase 2 will cause the mission to not end after it is shot down. https://www.speedrun.com/project_wingman/guide/xkm29#ch7Mission_12_Midnight_Light

Return - Crimson Squadron

In Return there is approx. 30 seconds between the mission update when Crimson squadron spawns and when the overlay appears (when Crimson 1 says “Crimson Squadron, engage. Avenge this land”). If all 8 (16 with double time) aircraft are shot down within these 30 seconds the dialogue will continue, the intro overlay will appear, and health bars appear, but despite the health bars all being fully depleted, the game will believe that the fight is ongoing as dialogue that play during the fight will continue as normal.

To avoid this softlock, simply leave a single aircraft alive until the overlay appears, after which it can be shot down to trigger the end of the mission.

Kings

The Kings softlock is caused by depleting Crimson 1’s first 3 health bars before they appear on-screen about 45 seconds into the mission. If this is done then despite being able to damage and shoot down Crimson 1 in phase 4, triggering his death dialogue and explosion, his phase 4 health bar will remain full, and the mission will not end.

The way to identify this softlock is if the overlay and a full health bar still appear for phase 4 after shooting down Crimson 1. To avoid it, simply avoid dealing enough damage to finish phase 3 before the health bars appear. https://www.speedrun.com/project_wingman/guide/h2i6m

Other Bossfights

As of writing, it seems unlikely a softlock in the other bossfights will affect speedrunnig. In my opinion, the only one that has a real potential of softlocking is Crosstalk squadron in Homestead, though they can already be destroyed extremely quickly as their intro overlay appears. The other bosses are all unlikely to have speedrun softlocks as they either spawn far enough away from the player that their overlay will have happened by the time your weapons are able to connect (Intercept Specialists in Clear Skies and Crimson Squadron in Cold War), or their intro overlay starts as soon as they spawn (Frost Druid in Wayback).

Frontline 59 - Faust ASMs

In the final mission of FL59, using ASMs to destroy the core of the CDV Roosevelt before intended, that is all other enemies being destroyed, will cause a softlock. The airship will become passive but still spawn its future waves of attachments and the mission will contiune playing normally as if it is still alive, but without being able to destroy the core at the correct time the mission will never end.

Simply don't use ASMs on this mission. The devs are aware of this and may be patched in future updates.