1. Tow weight. If you get a 34', you will need a diesel or 454 big block (or equivalent) tow vehicle. Smaller Airstreams you probably will not.
2. For a couple, a rear queen island bed is really nice. Single beds on each side make for lonely nights
. You can put a board across the isle and pull the mattresses together, but it is difficult to get to the bathroom or front of the trailer.
3. Holding tanks. Older models without holding tanks may limit your camp site opportunities. Blue tote able tanks are an option, but a hassle.
4. Length. A 34' may limit your camp site opportunities. I have owned a 34' Excella and two 25' trailers. I think the 25' trailers are perfect size. Not too small or too large, towable with most pickups, will fit in most campsites, has 4 tires (or 2 for 1950's trailers) instead of 6 for a 34 footer (more expensive to replace all of them). If you want to buy or replace awnings it is much cheaper for a shorter trailer. On the other hand, if you are going to park it in one place and not tow it much, a 34' may be just the ticket.
5. Known problems with some years such as the rear bath sagging problem.
6. Air-conditioning. In the South and other areas, a trailer is pretty much un-useable without it much of the year. Make sure it works. By the way, a single unit in a 34' Airstream in the South doesn't cut it.
7. And of course, condition of the unit verses what you are paying for it. I have found that it is much better to pay more up-front when purchasing it rather than having to fix and repair or replace everything later. If spare time is a problem for you, get one that doesn't need a whole lot of work. I have a 1953
Cruiser that I have been "restoring" for the last 10 years.
That's all I can think of now. Hope it helps.