Overcrowded servers=unexplained outages. DreamHost packs a bunch of people onto each server in order to accommodate their low monthly fees for shared hosting, and when someone–anyone–on a server misbehaves (e.g. sends out a bunch of spam, bursts their traffic/memory limits for any reason, whether legitimate or not), they penalize everyone by shutting down the server or limiting memory in such a way as to screw up your site.
Overcrowded servers=slow loading times. By the same token, if somebody else on your server has a bunch of unplanned-for traffic, your site is going to slow down. And since there are so many damn other people on your server with DreamHost, the odds of this happening go up. In my case, this happened quite a bit, nearly every week.
Their more expensive “private servers” are not private in the strictest sense of the word. If you get a private server from DreamHost, thinking that this will assuage the shared server-related problems you’ve been having, think again: a “private server” is just a server with less people on it, not shared with quite so many people, as opposed to being your own server. So yes, you’ll be able to request reboots of your server, but they cannot guarantee that you will have less problems with slowness and outages.
Somebody hack your .htaccess? Sucks to be you. If you ever have a crisis with your website that requires the assistance of DreamHost, it may take a day or longer for the support people to get back to you, if they get back to you at all. And if they do get back to you, it may just be with a link to a support wiki that you’ve already looked at and that was not helpful in the first place.
Low compatibility with other companies/sources of help. If you want to have somebody else help you fix your problem with a DreamHost-hosted site, there will be a steep learning curve involved while said person tries to figure out where “all your files are” because DreamHost organizes their files in a way different from other hosting companies. They also allow much more limited access to servers and do not offer cPanel access, which appears to be a preferable means of transferring data.