How to handle potential interactions when one-hot encoding? Let's say I have two categorical features: Movie, Director. I one-hot encode both the Movie and Director features for use in a linear regression model.

The problem is that two or more movies may be directed by the same director. i.e. a particular director's bit may be on for two or more different movies. Would this be a problem? Should I be combining movie and director into one feature?
You could combine these features before using one-hot encoding, and see if the performance is improved. But keep in mind, that it really depends on the problem each time. 

Generally, is a good thought to combine these type of features. CatBoost, a very good gradient boosting library, create such combinations and the results are pretty good most of the time. I would give it a go if I were you.