So I bought an expired domain which appears to have been the official homepage for a movie. I don't wish to use it for anything related to that movie, can I still use the site without getting into legal issues? Or should I take it down immediately? Or would it be enough to create a message on the front page saying that I am in no way connected to the movie?
The answer will really depend on the name of the domain and whether it reasonably has other non-infringing uses. Since you say you don't want to use it for anything related to the movie you might be okay, but if it was something like, "HarryPotter" you'd have a hard time using it in any non-infringing manner. On the other hand, a movie name like "Raging Bull" could easily have non infringing uses. So, the upshot is that it depends on the particular name in question.
Alright, I mainly want to use it for linking to another site. The domain is "name-name-movie" where name is the movie name. The domain name is pretty much pointing at the movie, but my content is not at all connected with it. If there was any issues, would I get a notice first, or would it be possible to get charged or sued right away?
It is not good that the word "movie" is in the name. The reality is that nothing could happen or you could get sued with no notice. I have represented a client who was sued with no prior notice for an allegedly infringing name although that is unusual. To me, these comes down to a business question. Is the small benefit from using the name worth the small risk of it becoming a problem. That is a decision you have to make.
Thank you so much for the great answer! I've decided to not use the site at all, so would it be ok to sell the domain name at an auction then? Or could even that get me in trouble?
You can sell it with no problem at an auction. It is the new buyer who has to decide if he has a non-infringing use just as you have done.