Bushes, hinges, wheel bearings, broken spokes (very common), badly worn rims because they're small and go through quicker, cracks around the seat clamp. If the headset is loose the lower cup *may* have stretched the head tube because it's lugless and unreinforced (Mrs Z's is like this). This cannot be fixed properly but Loctite will usually hold it between services. Avoid older ones with a 1" headset since you can't get a replacement stem now. The short wheelbase one is barely different to the LWB one though, so don't worry about that. The paint will probably be crappy and they cost a fortune to respray because they come in five parts, so you'll have to live with it.
If it is old or well-used, budget for new hinge clamp plates and bars - the "M" type in particular take a right pounding. Also budget for a new chain and sprocket on a high miler.
Provenance is very important, since most people in London with Bromptons seem to have had at least one stolen (Mrs Z's friend is on his fourth). Get the original receipt. An owner's manual is available as a £3 spare from any dealer and proves nothing.