I'm not sure why, but there seem to be very few early 1980s Airstream trailers out there. I'm guessing that AS was going through market difficulties then, but perhaps someone can enlighten us on that.
I agree with the other posts, put up some photos, maybe there's something we can see to give you some things to look at.
Also, there are a lot of Airforums members in Texas, so I would encourage you to look on the Portal page (the one you land on when you log in) for the little box on the right hand side that talks about getting help; an Airstream Inspector.
To your question, I am not aware of any particular problems form that time period, but as has already been pointed out, any thirty year old vehicle is bound to need work, and the help and inspector can give you can be invaluable.
Best of luck!
If it's to be, it's up to me.