To the original question, I think there are two categories of questions. One, are there design flaws particular to a given make and model? Two, what are the most common problems experienced in any particular vintage of Airstream.
An example of a design flaw is the rear end separation and frame "droop" in some longer, 70s era Airstreams. You can do a search on this and find ample information. Overall, however, I would say most folks think Airstreams have been fairly well built over the years and have relatively few design flaws. As for any mechanical system 30 to 40 years old, there are going to be issues caused by age, vibration, corrosion, metal fatigue, wear, etc. This is true of old trailers, old cars, old boats or pretty much anything else with moving parts.
Buying something vintage means making a commitment to spending time and money on certain things. There are two ways to look at this. One, you can see this as a money pit. Two, you can see this as an opportunity to improve on a good design.