Erm, rust, rust and more rust!
Generally Unos are tough cars, but can get tatty and also feel flimsy. The main thing to check for is rust. They can go just about everywhere, but worst places are front and rear inner wings/ arches, sills, floor pan and boot floor. These are all structural so will fail the MOT if bad enough. Outer arches and fuel filler panel can rust through, and if bad enough (jagged edges) can fail an MOT.
The other weak point is door bottoms. Most will be going rusty, but it's more unsightly than anything. It's quite common for the door skin to detatch itself from the door frame and flap around! If you find unrusty doors then you are very lucky and should inject lots of Waxoyl into the cavities immediately!
Gear changes can be a bit sloppy and rubbery, but the gearboxes do tend to go on forever. Often they just need new linkage bushes and a change of oil to make them feel better.
Engines are mostly FIRE units, though there are still some 1116/ 1301cc sohc and 903cc ohv engines still knocking around. FIRE units are tough and will normally outlive the car, most of the checks apply as per the Centos so you should be familiar with them. Sohc 1.3's (and mk1 1.1's) are also strong, but you'll won't find the sohc 1.1 in a mk2 unless it's fitted to a Selecta. Mk2 1.1's used the later 1108cc FIRE unit. 903cc ohv engines are ok, but can get tappety and burn oil with age. I don't know that much more about them to be honest.
Carbed Unos can suffer from 'icing' in winter, but this is normally down to the metal pipe from manifold to airbox being missing or the thermostatic flap in the airbox not being set correctly.
Distributor diaphragms often fail causing stalling and rough running. They are cheap and simple to replace.
Electrics can give problems, but that's mostly down to age and corroded connections. This normally affects lights/ indicators more than anything, but the Uno electrical circuit is quite simple (SX and turbo models excluded) so often just needs a clean up and some WD40.
Overall a simple car that if looked after will give you many years of service. They are getting old now, so all the usual age related checks as per any car apply. If the body is good don't worry too much about mechanicals as most parts are easy to get hold of (especially FIRE engines). Saying that, the older sohc engine is getting harder to find spares for now. Interior trim is made of unobtainium, so don't even bother asking a dealer if they can get parts. Seats, switches and door cards can still be found in scrapyards (getting rare now) or from people breaking Unos on the forum/ Ebay/ small ads etc.
Get a nice one and you can't go too far wrong
