I've been hosting with Dreamhost for over four years now, and am very happy with them. The one time I decided to move a site away from them (because it was using a ton of bandwidth and at the time their bandwidth limits were a lot lower than they are now), I had no problems at all. In fact, I ended up later moving that site back to them because the other host sucked.
I've always found them prompt in answering tech support queries - in the 4+ years I've been here, and with the dozens of domains I've hosted here, I can count on one hand the number of times tech support has ever needed a nag or reminder about anything.
As a professional web developer, whose clients often have hosting with other companies arranged before hiring me, I've dealt with more web hosts than I can count offhand, and Dreamhost have consistently been by far the best. They even offer support with things no other web host I've dealt with does, like user-installed CGI scripts. Every other host I've ever dealt with leaves you on your own with those.
With regard to domain name registration, transfers are in my experience processed by the registrar you're transferring TO, not the one you're transferring from, so if you've encountered problems there, it's probably with the new registrar's system.