Some people have stated on the forums that having the Steam menu open has helped them get through troublesome cutscenes. This is the easiest solution and is probably the first you should try.

If the solution above did not work, you may need to disable in-game cutscenes. Right-click the game in your Steam library, click "Manage", then click "Browse local files". In the folder that pops up (C:\Program Files (x86)\Steam\steamapps\common\Disney Epic Mickey 2, or something similar), create a file called ConfigOverride.ini, open it in Notepad, and put in the following text:
This should cause the game to skip most of the in-game cutscenes at the beginning of levels. Afterwards, you can delete the ConfigOverride.ini file and reboot the game to turn in-game cutscenes back on. You'll have to find whichever cutscene you missed on YouTube to catch up.

• Make sure that you're using this fix if you have a CPU with more than 4 cores.
  
• Consider removing 60fps hacks if you're using one. Issues have been observed when uncapping the framerate, such as broken Oswald AI and problems with moving platforms.
  
• If all else fails, it never hurts to have Steam scan your local files.

If none of these solutions worked or if you found another that worked for you, please let me know!