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: 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 timeline of the movie is quite strange; April obviously got her job back and made advancements in career, living in a sweet two-floor loft. At least -some - time must have passed, many pizza deliveries and all that, but Shredder just woke up from the pile of garbage he ended in at the end of the last movie and the Foot hasn't attempted any reaction or organization yet, implying it is set mere hours after the first movie.