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 Frank Mercer is talking with the family about their Generic Pancreas Unit to sign the contract, the paperwork he gives shows the wrong price ($~660,000) versus the quoted $618,429 and the wrong body part (pancreas versus kidney).
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.
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.
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.
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.