First and foremost, the bad stuff is lack of really quick support. They promise to answer within 24 hours but they have been bad at keeping that promise for many months now. They say they have hired additional support staff and they are being trained now, but the lack of quick support is one of the biggest pains at the moment. DH offers support by email only, plus phone callback only if you have one of the bigger plans AND you're in the USA.
The other big issue is that DH has grown immensely in the past months, and it appears that DH has not been able to maintain the service quality. Some servers run slowly sometimes, there have been mysterious network outages, mail servers are overloaded, and so on. DH says they're working on improving this too, but we're not seeing great advances being made yet.
That's the really bad news. The better news is that DH is still a great place to be. DH has one of the best price/value offerings around, and many customers are complaining but staying after all because they love DH so much anyway.
This is my impression of things at the moment. I don't have any problems with support, but I notice the strain on the servers sometimes.