Problems? I'd say most people have problems with the way the company is run, not really the technical side of things.
A few of things that come to mind:
A. Prices way too high, at least in Dayton, Ohio. $103 for digipic 2000 and 2 HD-DVRs per month is ridiculous. When I called up about it they offered me 3 months at half price, but could not match what friends of mine had just signed up for (Digipic 4000 for $55 per month).
B. Add new TV channels at a faster rate, especially HD. ESPN2HD has been out for 20 months now yet we still have no seen it. NFL Network/HD is not yet picked up. ESPNU is not picked up.
C. Offer a set top box that allows you to connect an antenna for the local HD channels that you have been unable to come to an agreement with. In Dayton you have an agreement with ABC, CBS, and Fox. No CW, no NBC. With a simple set of rabbit ears I could have picked them up.
D. Stop lying about your internet speeds. You claim they are up to 10x faster than DSL, when in reality in the Dayton market your downstream speed is the same, and your upstream speed is about 1/3 of DSL. I know you put the disclaimer "based on national averages, may not be the case for your area", but I still think that is crap. That is nothing but a play on words, when in my area that is nothing but total BS. I'm sure it sells a lot of people, but in my case it turns me off of TWC because I feel like they are lying to me.
In the end, I think TWC will begin losing customers as a faster clip due to their inability to add new channels while keeping the costs down. Time Warner is already the most expensive TV provider in the country, and they are also the company with the least amount of channels. I left TWC due to those 2 reasons, I'm sure more will begin to realize now with this whole NFL Network dispute.