I just converted my email from being handled by Dreamhost to Google Apps/Gmail yesterday and I'm surprised nobody's mentioned this problem here yet.
Anyway, I followed all the instructions to the letter. I set up all my accounts on the Google Apps page and was even receiving email on my client (Thunderbird). However, I was having no luck with sending mail via the SMTP setup. Some Dreamhost customers (not all) have an issue where the SMTP server issues a "5.7.0 Mail sending denied" error. Even from within the Gmail web application, you'll get "You can't send mail yet" if you try to send mail. Apparently, while it's a problem with Dreamhost customers, it's fixable on Google's side. It seems to be a fairly common problem and nobody's saying exactly what the cause is.
So go to this Google Group, join it, and post on this thread that you're having this issue:
There are Google Apps Advisors that scan this thread and make the fixes on the affected domains. They're not quick, so have a bit of patience.
One other thing I noticed was a bit unclear from the instructions is that when performing email client setup, you can't use your own domain in the server names for incoming or outgoing mail (i.e. mail.example.com, imap.example.com, smtp.example.com) - you have to use Gmail's (i.e. pop.gmail.com, imap.gmail.com and smtp.gmail.com).
Hope this helps somebody and saves you a bit of time messing around.