My own experiences, as a frequent borrower of the petrol 500 and owner of a 500e is that these are great cars, especially if you need to park on town streets - you can use spaces that nobody else can fit in!
What this is not is a performance car, and once you relax into the idea, they're quite pleasant to drive.
I'm 6'3" and have come out of many 3+ hour drives in a 500 with no aches or pains. There's a lot of headroom, despite the small size. (I also favour an relatively upright driving position).
There have been five engines used in the 500 models sold in the UK, but you get different power levels depending on year and trim. These are:
1.2 FIRE, around 70 bhp in all versions
1.4 FIRE, 100 bhp in regular 500 (very rare). From 135 to 200(!) bhp in Abarth 500.
0.9 SGE "TwinAir" 2 cylinder turbo: 85 and 105 bhp. Discontinued in 2018.
1.3 MultiJet diesel, 75 or 95 bhp
1.0 GSE "FireFly" 3 cylinder turbo + mild hybrid, 70 bhp. The current petrol engine.
These are all very reliable engines. The 2018-2021 1.2 engines lacked torque due to some heavy-handed compliance measures, but the earlier 1.2s are fine once you realise that this is not a car for putting down lap-times. TwinAirs use FIAT's MultiAir variable valve control system, which uses the engine oil as a hydraulic fluid, so a car that has had its oil changes done on schedule is good to see.
The newest, 500 Hybrid, models use a new-to-Europe 1.0 engine, but this has seen a lot of work in Latin America already, and is proven to be reliable there. I wouldn't worry about it.
The automatic option is called "Duologic". It's an automated-clutch system, rather than a traditional torque-converter automatic used in bigger cars. I drove one a long time ago, and it's actually not bad. Again, this is not a performance car, and its action is very much in the "not a performance car" mould. These are very rare, though, and I think all are paired with the 1.2 engine.
Lounge (the middle option) was the best value trim when new. Above that was Sport, and the top-trim Collezione and Dolce Vita. There's also particularly luxe model made in collaboration with Italian boat-builder Riva that ran for a couple of years, and the one-offs with Italian fashion brands (Prada, Diesel, Giorgio Armani).
500s are reliable in general, but negligent maintenance can kill any kind of car. They seem to be good on brakes, and there's not really any problem with clutches, but these tend to be a low-mileage kind of car.
Speaking of, the TwinAirs don't get "awful mileage": they just fall a lot short of the stupendous official figures that they posted on the NEDC driving pattern (70 mpg!). My real-world consumption with a 105 TwinAir was about 48 mpg over the course of two weeks - for a 2011 petrol-engined car, that is still very, very good. A friend owned the cabrio version for five years and got around 40-45 mpg from it (cabrios are always higher consumption due to extra weight and drag).
The 500 is a close twin of the FIAT Panda (and the Lancia Ypsilon, a car that was briefly sold in the UK as "Chrysler Ypsilon" from 2012-14). The 2008-2014 Ford Ka is a mechanical copy of the FIAT 500, designed and built for Ford by FIAT - only the bodywork and interior trim is different between these cars (early 500s had a different rear suspension to the Ka, but the Ford specification was rolled in to the 500 from about 2010 onward). Knowing this fact makes it very easy to see which reviewers allowed bias to cloud their assessment of the car. I remember one publication recommending the Ka on the basis of having a "solid, proven drivetrain" while elsewhere casting doubts over the 500's mechanical reliability.