(Full disclosure: my husband and I have both worked for Charter - me in sales, hubby in repair, then tech support - when we lived in Fond du Lac)
The fact that the other sets in the house don't have that problem doesn't necessarily exclude the possibility of it being that particular outlet itself.
The easiest way to rule out a problem with the outlet is to try connecting a different television to that outlet. If that solves the problem, it's likely the TV, and Shipley's right on - either a new connection or a new television and you should be good to go.
If you have the same problem even with a different TV, it could very well be the outlet. In that case, schedule a service call, but add wire maintenance to your account first so you don't have to worry about being charged for a service call. Unless something has changed in the 11 months since I left, all that matters is that you have it on your account at the time of the service call - you can have it removed the next day and you'll only be charged for the days it's actually on the account (just keep in mind that if it is the outlet and you're a renter, they may tell you to have your landlord fix it).
Take this next part with a grain of salt because as I said, I was in sales (soooo not a techie) and this may be off-base, but if your TV has a component input, you may also be able to bypass the coax input on the TV through the use of an RF modulator - coax from the wall to the modulator, then component from the modulator to the TV. Hubby's asleep, but I'm sure there's a techie here who can correct me if that won't work.