Now that mission instapasses/skips are a possible subject of new category, I will be listing the known glitches in this thread, separating them by all 3 districts and with 3 categories (IP = instapass, skip and other)

Downtown:

• [IP] Happy Gas Smash: Start Bank Robbery, blow up the shark and pick up the phone approximately 21 frames after job complete text appears. Need to die or get busted to update the mission counter. Video demonstration:

• [Other] Radio Za-Za: It is possible to dupe Radio Zaza through the pizza cake phone. If you get busted or wasted, it will first fail the mission but then complete it, granting multiplier and score. Unfortunately this doesn't add to the mission counter, so it cannot be used as an instapass.

Residential:

• [IP] Science Friction: There are multiple ways to instapass Science Friction, but one good way to do it would be through Labrat's Plan mission (route used in AM category). Upon completing Labrat's Plan, if you wait long enough for mission counter to add up but for mission to not fully finish, you will instapass Science Friction upon phone pickup. Need to die or get busted to update the mission counter.

• [IP] Greatest Hits: Start Science Friction and get the Pickup from redneck area. Destroy the pickup and start Greatest Hits before Science Friction fully finishes. Need to die or get busted to update the mission counter. Video demonstration:

• [IP] Valdez Alert: Upon completing (or failing) Distraction Action, you can pick up Valdez Alert phone to instapass it. However, if you pick it up too quick (before distraction action job complete gets added to mission counter), it wont ever update the mission counter for Valdez Alert. Need to die or get busted to update the mission counter.

• [Skip] Operation Z: Upon completing the mission Gang Car Bang, if you pick up the phone at perfect frame, the game will spawn the Limousine and you can continue the mission from that. Triggering the phone 1 frame earlier will cause game to crash, and 1 frame too late will start the mission as normal.

• [Skip] Redneck Attack: If you place your car well enough between the 2 yellow phones, you can dupe Redneck Attack through Labrat's Plan mission. This will cause the 2 minute timer for protecting the generators to be halved to 1 minute. (2 timers will show but first one disappears after first minute).

• [Skip] Fire Truck Fun: There are couple of ways to dupe Fire Truck Fun without game crash [to be updated]. Doing so allows you to get Fire Truck flamethrower without having to steal the yellow van, as the guy near the garage will already be waiting for you.

Industrial:

None! However, industrial also has the perfect frame trick which allows you to start another mission before previous one fully finished. So far all tests have ended up to crash, but there are a lot of combinations left to be experimented.

I will be updating this list as new instapasses/skips are discovered. Also if you happen to be interested at searching for more of these, then definitely go for it, more people means more discoveries.