Plot hole: When Henry rings Maurice's doorbell to give the bad news about Sarah's fatal illness, Maurice and Sarah are upstairs in the bedroom. Maurice approaches the window and looks down while we see Henry looking up in his direction. That he walks away without trying to make contact makes no sense.
Factual error: Just as Ralph Fiennes is getting out of a car to run across the road you can see, just as he steps out, road markings that were not around in the mid forties and that weren't on the road in a shot just previous when you could see the road behind Fiennes in the car window.
Continuity mistake: When the bombing scene is shown the first time Maurice breaks through the railing of the landing between the first floor, where he and Sarah were, and the ground floor. When Sarah tells her story and the bombing scene is replayed, we see her running down one full flight with an intact railing. She keeps running down and then comes to the spot where Maurice is lying on the steps. That means the second time there is one flight too many.
Continuity mistake: In the last scene of the movie, after Sarah's cremation, Parkis's boy Lance walks up to Maurice. Then he puts his hands in his pockets (we can't see the hands but it's clear from the way he moves his arms), but when the camera angle changes his arms are hanging down.
Continuity mistake: When the bomb explodes next to Maurice's place he gets blown off the landing of the staircase. The way he 'takes off' he would have fallen on the ground, and there's no way that he would have landed as Sarah finds him, on the stairs and with his head pointing upwards.