I'm running a Facebook application on Dreamhost.
Here are my stats for the last 7 days:
Successful requests: 1,734,747
Average successful requests per day: 247,820
Failed requests: 8,396
Distinct hosts served: 3,217
Data transferred: 3.54 gigabytes
Average data transferred per day: 517.94 megabytes
As you can see the only issue I have is Failed requests due to Facebook's API being sometime too long.
If I read a user's stream to get a bit too much posts (for e exemple posts for last 12 hours) Facebook can be so long to answer that the server's security routine kill my script because of timeout.
If you code well, and are ok with less than 0.5% of request failure (no doubt you'll have less than 0.01% if you don't make big FB requests), then there's no issue with hosting a facebook app on dreamhost.