Kipps travels by train, with antimacassars showing N&CR. This can only be Newcastle & Carlisle Railway, but this was absorbed into the NER in 1862, 40 years before the film's setting. Also, the locomotive is a Southern U class, which did not venture that far north.
While Mr Jerome is initially trying to dissuade Kipps from staying in town, there is a point where Kipps tells Jerome, "I don't expect to be finished until Friday at least." Even seen from behind, it is clear his mouth continues to move after the sentence is finished.
At 54 min 40 secs, Arthur Kipps puts down his axe to tear wallpaper off. After tearing the paper off he steps back 2 or 3 steps and reads the inscription. The next shot shows him holding the axe again but he never bends down to pick it up.
When Arthur Kipps (Daniel Radcliffe) first reaches Gifford Arms Inn in Sam Daily's (Ciarán Hinds) car, it is raining heavily and Arthur is shown with his clothes wet. When it cuts to the next scene where Arthur talks to the innkeeper Fisher (Shaun Dooley) at the reception counter, Arthur's clothes are suddenly dry. In the next scene still at the reception, his clothes are wet again.