Grabbing red pins in various ways can lead to some interesting things in this game. There may be more out there yet to be found but so far, two very useful glitches involving grabbing of red pins are as follows:

1. "Ghost mode" Ray What does it do? Ray is able to walk through walls, fall off of walkable surfaces but will die, most agents/nurses will disappear if you approach their areas from this out of bounds limbo state. How to do this? When a cutscene is triggered, either by sticker placement or moving Ray through a trigger point, if you grab a red pin within a certain amount of time (this can vary - some are more precise than others, most seem to be pretty lenient though), then when you get out of the cutscene Ray will be in his weird limbo state of being able to pass through a lot of walls.
2. "Invincible mode" Ray What does it do? Ray is immune to agents/nurses, they will still see him but won't be able to grab and kill, you can fall off the walkable surface into the void but most of the time Ray will not die. How to do this? While hitting and hold the mindread ability, quickly (but not instantly?) tap the launch arm button directed at a red pin. If it works you'll see the spaghetti arm kind of reach out but not actually grab the pin. On PC, you can re-map the mindread & launch arm abilities onto one button (R2 in the clip below) and then you just use that combined button to reach toward a red pin. No timing of inputs is necessary for this version.