If it's a leasehold flat ask how long the lease has to run, how much the service charge and ground rent is. Ask what work has been done on the building and how it was paid for if the vendor was living in the blcok at the time - what you want to know is if major repairs have been carried out, stuff like the roof etc and whether the cost needed topping up by the flat owners. Whether it's lease or freehold there should be some sort of fund for repairs to the structure. otherwise nothing gets done until everyone has put in their cash and that could be thousands each for something like a roof
Whether it's a flat or a house check whether the outside looks in good repair - if the door frames or window frames are wood you can gently press them to see if there's any give. There shouldn't be. But be gentle because if you damage the frame you'll be in bother!
Ask about parking. If it's a flat does it come with a parking space, have they had any problems with people using their space without permission, is there space for visitors. If it's a house and there's no drive is the on street parking free or is there a permit scheme - if so how much.
Ask about boilers or central heating systems. When was the boiler put in, is it serviced, do they have proof of that if it is. If there are radiators have a good look at them. Any rust or signs of leaks?
How much is the council tax.
If it's a house and they've had any building work done ask about planning permission or building regulations. If they've extended they probably needed planning permission unless it was in the past couple of years when the rules changed. If they've done internal work, like making two rooms into one, they should have proof that it met building regulations. Anyone showing their house who'd done that work should have plans and certificates ready so don't be afraid to ask.
Ask what the neighbours are like - you may get a 'oh very nice' but you'd be surprised how many people aren't ready for that one and can sometimes slip up if there have been problems.
Oh, and coming from someone whom has bought and sold 6 times, don't hover at the doorway in rooms. Go in, ask if you can open cupboards and windows. You're looking for doors not fitting the frames or windows sticking - that can be a subsidence problem, which isn't always a big issue but could need a negotiation on price and would definitely want checking by your surveyor - anyone who's not hiding something will be fine. I've even asked if I could run the bathroom tap and flush the loo as my first house had the noisiest plumbing and I wasn't getting caught again - never been refused. Run your hand over walls at ground level - you can sometimes feel damp or wallpaper that 'gives' which may be hiding a problem.
When I was showing people around I always offered them the chance to look around on their own. Always ask if you can look around again if the offer isn't there - even if the owner wants to come with you it's a chance to look more closely.
And, most of all don't be distracted by chit chat. If you're chatting, you're not looking so be polite but try to zone out small talk.
Finally, ask if you can come back for a second viewing and take someone with you. Don't be rushed - if this one goes another will come along.
Good luck.