Hello and welcome!
A few pointers I have:
1) It's on Audi dealer plates: always nice to see as usually means it's not been accident damaged and generally cars with dealer plates are the nicer ones.
2) On the face of it, it looks very straight and unmolested on the outside.
3) The seats have a lot of staining: I'd want either the dealer to do a full wet-vacuum clean on them or give a discount as the car is top money (not unfair if it checks out, but at the top end price-wise). The good news is they will clean up like new.
4) The 'soft touch' coating around the light switch has started to wear away so expect the same around the climate control and the stereo. Not massive problem but if you like detail, it's tricky to resolve without replacing parts.
5) The 1.4MPi petrol engine is prone to 'piston slap' if not looked after. It should be sewing machine quiet: you want to hear it start from stone cold: there should be no tapping sounds. Looked after though and they are brilliant: can do big miles and the 1.4MPi is the sweetest handling of all A2's due to the very light engine and gearbox. So far, my favourite of the range.
6) The gear-change should be exceptionally sweet: these have a lovely gearbox so any stiffness in the change means the gear-shift mech at the gearbox end needs some maintenance.
7) As stated above, check the front lower wishbones. Regardless, if you take ownership, have them Waxoyled (or Dinitrol'ed) to prevent them rusting from the inside out in the future.
8) Make sure all the of climate control functions work: these can give mild problems although all four of my A2's over the last few months have worked fine.
9) You'll hear about E10 unleaded coming in next year: this is raising the ethanol content from 5% to 10%: don't worry, the 1.4 is O.K. on this, unlike the 1.6FSi's.
10) The car should be sitting on alloy wheels. Plus they're cheap aftermarket hup-caps. My betting is you might even find the wheels aren't A2 as not many in the U.K. had steels. They're as likely to be Polo / Ibiza and so on. Therefore check that the tyre sizes printed on the tyres match with one of those inside of the fuel filler. On the other hand, there is at least one Continental tyre there: people that fit matching sets of quality tyres rarely neglect their cars. Similarly, always be wary of cars running a disparate collection of individual budget tyres: people that do that are hardly likely to then specify the very best engine oils etc.
11) A2's wear their wiper arms out. As they wear they drop onto the screen and scratch it, starting at the bottom.
@depronman here rebuilds the arms at not much money to a very high standard, but do check the screen as it's usually not possible to polish the marks out much.
12) Make sure everything is in the lower boot caddy: from memory you should have: jack, wheel-brace, locking wheel key, screwdriver, one spanner, hopefully a hub-cap puller (wire thing: a circle with a hook on the 'side' there to pull off the alloy wheel hupcaps. £5 to replace), a 12v compressor and a large white bottle of Audi tyre gunk.
13) You should have a false (double depth) floor in the back, a retractable load cover and ideally a set of carpet overmats.
14) It should have two remote keys (check these work), a plastic white key tag, and the main owner's wallet.
After that, you're doing all the regular used car checks, which is where your RAC man comes in. I could write several pages on that, but no-one needs to be wading through that on a Monday morning
Oh yes: check the glovebox works O.K.: it should have a light inside that comes on when you open it (but shouldn't be on all the time). Glovebox handles and light switch mechs sometimes give problems. And on the right hand side, bottom of dash area, make sure you have the fuse cover in place: they often break off. Again,
@depronman does a fix for this if broken, but if it's not in place have a hunt around the car for the cover: they often are put in the glovebox or a door pocket.
Good luck! And don't worry if this one falls through or doesn't feel right. At that price you can afford to be very picky and cars are always cropping up on here at very fair prices.