I've been living in a travel trailer most of the past seven years. I think the major downside is that those trailers are usually not equipped with the sort of quality accoutrements for someone to live in full time.
What I mean is the mattress that comes in one is cheap, and will completely fall apart before long. The light fixtures in mine all need to be replaced now, they're much more cheaply made than typical light fixtures. The plugs and switches are very very crappy. Do you get the idea? Now granted, these things are not terribly expensive to replace, but then again I can replace those things myself.
The other major downside is a lack of storage space.
The major upside is one is not paying the rent for an apartment or the high cost of utilities for one either.