I doubt that you would get in trouble. The worst-case scenario would probably be a request from the copyright holder (or their lawyers) to remove the image. If that ever happens, I'd suggest that you should probably comply (even if you think that "fair use" rules should apply).
Of course, it also depends in part on where the movie was made. This article on Copyright & Fair Use may help for US Copyright laws. However, copyright laws vary by country.
As regards Stack Exchange liability in case of copyright infringement, they have that covered in the Stack Exchange Terms of Service, section §3 where it states that we are all responsible for ensuring that we have the right to post the content that we contribute to the SE network.
Note also, that the Terms of Service state that any content that we contribute to the SE Network is then perpetually, and irrevocably, licensed to Stack Exchange under the terms and conditions of the Creative Commons Attribution Share Alike license (CC BY-SA). This is something to be aware of if you are thinking about sharing the results of original research on this (or any other) SE site.