Plot hole: The Bishop in the film is performing the duties you would expect of someone in his position (giving mass, hearing confessions, performing weddings etc.) He has his own private chambers in the cathedral, refers to Robin as 'the boy I knew' and talks about hearing his Father's confession four months earlier; so he's been around for a while. The problem is the credits refer to him as the 'Bishop of Hereford'. No explanation is ever given for why the Bishop of a city 100 miles away is living and working in Nottingham rather than looking after his own diocese; or why the Bishop of Nottingham isn't around to look after his. (The Bishop of Hereford was an enemy of Robin Hood in the original ballads, and it's likely the filmmakers just gave that name to the Bishop in the film due to its familiarity, without thinking about the plot hole this creates).
Plot hole: On arrival at the Summerland castle the Polar Bear King becomes human during the midnight hour (as part of the spell) and performs his husbandly duties with his carry-on wife. Why did he not become human during the journey from Winterland to Summerland which took several days? (00:32:40)
Plot hole: The helmet design is rubbish. The eyeholes are far too small - that close to the eyes the divider between the eyeholes would block almost a third of the wearer's vision. He would hardly be able to see what was right in front of him - and it is not too close nor too narrow to fall into the "blind spot" between the eyes. This is not a character error by Peevey - the helmet design came from the original plans - it is even shown in the German propaganda film!
Plot hole: It's never really addressed or explained how Shredder survived his death in the previous movie from being crushed in a garbage truck.
Suggested correction: It didn't really need to be addressed, and thus is not a mistake. His hand emerging from the junkyard is enough to show that he survived his apparent demise at the end of the last film.