Other mistake: Not a mistake with the game but a mistake with the booklet. In the "History" section, it says Chris and Jill defeated T.A.L.O.S. in 2002, when in the game, and in RE: The Umbrella Chronicles, it's established that they defeated him in 2003.
Continuity mistake: Nearing the end of chapter 1-2. Before the cut-scene where the player finds the dead Alpha team and the dying DeChant, both Sheva and Chris are required to kick a door open. But when you activate the cut-scene, you can see that Chris kicks the door by himself.
Continuity mistake: During the cutscene where a Majini places the Plaga into the other man's mouth, the table shows there is no TV, however, when gameplay with Chris / Sheva begins again, a TV is on the table.
Continuity mistake: During most of the cut scenes, Chris and Sheva will be equipped with handguns, even if you do not have any handguns in your inventory.