Well, my parents have had A-classes for a long time now and all four have been autos. The first one (an S reg A160) never gave any problems gearbox wise and the same goes for the 52 plate A140 that mum has kept. The 04 plate A160 and A170 CDI were both quite troublesome though.
I've been driving the A140 auto for about 18 months or so and I think it's a very pleasant little car to drive. Economy wise we reckon that it gets anywhere between 34 and 42, depending on conditions, how many are in the car and so on.
If you're looking at an A-class listen for any clunks when driving. As Howard says the springs are prone to breaking, quite regularly too if the surfaces are rough, trailing arms get damaged and drop links start knocking too. When doing low speed parking, a lot of cars will make a clonking noise from the steering, this is due to worn universal joints on the steering column which is rather poorly designed. As a result, you may well find A-classes which have had columns replaced and even racks in some cases.
Bodily, they can rust,check the rear wheel arches, the bonnet, especially next to the grille, and check the door bottoms too as plastic bottoms can get dirt into them and cause rust.
The interior plastics on the early cars can feel flimsy but generally they seem to last relatively well. The cupholders can break of their own accord though, and the coloured finish on some plastics can rub off. When you go to look at one, wash the rear window, as often there will be a leak in the headlining or in the plastic just above the parcel shelf. A smell of petrol inside will often indicate burst jubilee clips on the fuel line, and be prepared for all manner of strange electrical maladies such as windows which refuse to open (or shut), random warning lights and other little niggles. If you buy one with a sunroof, it's a lovely feature during the summer, but if they aren't properly maintained, you may well find a nice little puddle on the driver's seat.
In terms of spec, try to get an Elegance or Avantgarde. Elegances all have air con, whereas the early Avantgardes didn't always, though they did have half leather. Elegances ride slightly better and don't have quite such a harsh ride, but it's not really that big a difference. The earliest cars have a push button release for the bootlid which can be a complete pain in winter if it freezes up, so try to get a car with a pull handle. Also, some cars may well have an armrest, which isn't too much of a problem provided the car is an auto and you tend not to bother with the handbrake, if not, it can be a real pain when it's down.
If you can, try to buy a facelift car, they really are far better and have a much nicer looking interior, wood trim on Elegances. As regards engines, the A140 is quite alright a lot of the time, but the A160 petrol or the A170 CDI are nippier and the A160 is no thirstier than the 140 in the real world. In terms of transmission, autos get a bad name, but from my experience aren't always a massive problem, avoid clutchless manuals like the plague, and manuals are generally trouble free.
I hope this helps, and there's a lot I've missed out, but I reckon it gives you a good idea as to what the cars are like, and if you have any questions feel free to ask.
Don't buy any A-class without a full history and try to find one which has evidence of only ever having had Mercedes parts fitted.