I have my tank and tv on the same circuit. Wasn't my original plan, we wound up moving our entertainment center to an otherwise tank-only circuit.
The reviews for our tv said it would hum slightly (regardless of electronic ballasts) so when we bought the set we also bought one of the Monster power filters and it is doing a great job. Can't compare to not having the filter, but we notice absolutely no interference issues. (And it made it very convenient to power up the system - with a ton of labelled outlets on the back of it.)
It isn't cheap, but then again neither is running a new dedicated circuit. And for what it's worth, I've even read that dimmable lighting can create enough noise on a circuit to mess with a tv... I know for sure a refrigerator motor will.