Continuity mistake: When the Dark Aster enters the atmosphere at the end of the film, its wings untwist as it descends, in most of the scenes afterwards and the hologram the ship's wings are still twisted, then later during the battle they untwist again.
Continuity mistake: When Quill and Gamora first meet and get into a fight, Gamora grabs the Orb Quill is carrying and runs. Quill throws a sort of laser-based "lasso device" that snares her legs and causes her to fall. She pulls it off, and immediately in the next shot, it's vanished from the ground between cuts. It also had mechanical components, so even if the laser vanished, the mechanical pieces should still be on the ground.
Other mistake: At the end when the ship crashes that part of the city is leveled - we see injured people, but no one is covered in dust or dirt thrown up by the impact - everyone is clean.
Continuity mistake: During the prison break, Gamora kicks a guard with a black baton that she needs to take. When she first kicks him, her hands are up, and the next shot she's grabbing his wrist and the baton is in front of her body. In the next shot, it's behind her head and the next shot the baton has moved to a 3rd position, across her leg.