When Jake and Remy fight in the derelict apartment and Remy wins, he is wearing street clothes. But when, at the end of the film, he is shown on the stretcher attached to the Neural Network machine after, in reality, losing this fight with Jake, he is wearing the combat clothing that he wore in the Union headquarters building, which was when he was in a dream state.
When they get on the subway train (TTC Bay Station) the car they enter is either a Hawker Siddeley(Urban Transportation Development Corporation) H5 or H6. After the first interior scene the car becomes a Bombardier Transportation's T1 for the rest of the scenes.
When Remy stops typing he takes the binoculars off the table and looks out the window. When the camera shows the pages he has written on the table the binoculars are near the pages on the table. But when they switch back to Remy he has them in his hand again.
Jake and Frank are denied access to the reclamation room because they lack an Artiforg to scan and are forced to scavenge one from a dead guard, despite being surrounded by dead Repo men who presumably had numerous reclaimed Artiforgs already in their possession.
In the scene where Remy is on the typewriter typing and Jake walks into the room, you can see words on the paper. After a camera cut, the words are gone, and a blank piece of paper is in the typewriter instead.
The goof items below may give away important plot points.
When Jake takes a look at the draft of Remy's unpublished book The Repossession Mambo, while Remy is carried off on a stretcher at the end of the film, you can see that the page Jake takes a look at contains a spelling mistake in the title itself. The word "Repossession" is missing a fourth "s" (being spelled "Repossesion" there).
When Jake hands Remy the yellow syringe, in the pink room, he has already removed the cap. In the next scene you can see Remy holding the syringe with the cap still on and then removes the cap again with his teeth. Note this is a dream sequence so the glitch is in the MI5 machine!