I work at a range. I am by no means an expert, but I do get to see lots of weapons firing lots of rounds, and get to fire more than a few myself. My experience with HK's:
Good:
Some are extremely comfy to shoot (p30, p2000, HK45).
Seem to be well designed and put together. Whenever I take apart the rental guns, the HK's fare the best. Very little fouling anywhere other than the barrel and feed ramp.
Very reliable, and break neither more or less often than the Glocks, the CZ's, and the SIG's.
Accurate. Nothing special, but more than adequate. Perhaps a little better than a Glock.
Fully ambidextrous options.
Mostly well-placed controls, slide stop, mag release, etc... all good. I don't like the safety/decocker on the USP, but many other people do. The mag release is kind of wonky, but if I carried one, training would make this a nonissue
You knew it was coming...
Bad things:
Trigger. I don't like it. Every one I've handled has had a gritty, heavy, stacking trigger pull in both SA and DA modes. They do have a massive array of other trigger options, so one of those might suit me better, but haven't had the pleasure yet.
Price. If I really wanted one, this would make no difference. None at all. I'd just have to save more. Other polymer pistols do tend to be much cheaper, but that's the market. Don't like it? OK, do what I did, and don't buy one.
CS/Company attitude. They don't really seem to be concerned with the civilian market. That's their choice, as it is mine whether or not to buy their wares.
And the biggest reason I don't have one? I just don't really want one. I prefer CZ's. I prefer 1911's. In polymer I prefer M&P's and XD's. (Glock? meh.)