Sounds like your movies are buffering, how fast is your internet service?
If you have a Broadband Internet Service Provider, contact and have them check your connection speed.
If you have a slower DSL connection like me, then you will need to either download a lower resolution version or find a faster Internet Service Provider.
How full is your Mac Mini's Hard Drive, it will read slower as it gets full.
If that is the case, you may want to move your iTunes media library to a larger External Hard Drive.