I have two of these of different ages, and a few precautions will help you avoid a lemon.
1. See some provenance. There are many, many stolen Bromptons out there. The original shop receipt is good. An owner's manual can be purchased for a couple of pounds from a Brompton dealer and is no proof of ownership.
2. Check the condition of the rear hinge by waggling the rear triangle. If there is much play it *can* be fixed, but allow £50 or so foir a dealer to sort it out with new bushes. Ensure you find a dealer that has the special Brompton reamer.
3. Check for a loose headset. It may not just be adjustment - the head tube isn't lugged and can stretch with time, causing the lower cup to come loose. This can be fixed with Loctite 660, but it's best avoided.
4. Rust is rarely anything other than unsightly - the tubing is thick walled - and Brompton paint jobs are notoriously soft.
5. If you're over about 5'8" you need the extended or telescopic seatpost.
6. The rear brake and gear cable should sit closely together when the bike is unfolded and should not foul the chain. If there's a problem, they're the wrong length or have been incorrectly routed. Budget for new cables (£18 for a complete set).
7. If the bike has been used a lot, budget for new handlebars (£20) and hinge clamp plates (a couple of pounds each). They fatigue, and Brompton "M" type bars in particular are under huge strain.
8. Broken spokes are really common, so check.
9. Check all gears engage properly. Stamp on the pedals in top gear if it's an older Sturmey-Archer hub - a worn clutch or planet pinion pins will allow it to slip. However, the torque on a 16" wheeled bike is low and they usually last forever.
10. Check the condition of the folding left pedal. Replacements are £35. You also need a 24mm socket to fit ot remove one. If the reflectors are broken off, don't worry - they come as (cheap) spares.
Enjoy your Brompton and don't let it out of your sight when out and about.