Bodywork and interior fittings always falling apart, but there was very little that I couldn't fix myself with gaffer tape and/or superglue.
Rear brake drums fell off (yes, really) a few times, but they were easily and cheaply fixed.
In the end rust got the chasis and despite the fairly low mileage (nearly all of it in the last three years of its life (with me) ) that was that.
For:
Nice little car to drive, fairly comfortable even for tall people like myself, after-market (no other option) radio sounded okay, and of course - convertible!
0 - 60 in well under a year.
Wasn't really interested in petrol, so huge mpg was had out of the thing.
Boot space adequate and spacious if back seats removed (very easilly).
Reliable if a bit shoddy, but with very little that could go wrong. Never ever failed to start, although it did occasionally need the ignition to be sprayed with antifreeze before the key would turn.
Against:
Built out of nothing stronger than bacofoil, so crash=death.
Unusual gear-stick arrangement to some getting used to.
Only drank four star.
I had a heavy crash in my 1988 2CV and it annihilated a 2003 Micra (wrote it off). It depends where you hit a 2CV as to whether it performs well or not. The chassis (assuming it contains mostly metal, not rust) is surprisingly strong on a dead straight front impact, holding the engine and gearbox in place, and dissipating most of the impact before the bulkhead gets involved. I would not like to be involved in a corner-to -corner accident though, let alone a side impact.
The use of a replacement chassis is a matter of contention with some insurers, so if paying for a re-chassis, check that the galvanised ladder chassis (without Citroen intended crumple zone) is actually covered without being classed as a modification to the vehicle.
The truth is that in general terms, you are so scared of being hit that you drive more carefully than you would in a new car with all the safety features that give you a sense of being totally impervious to all danger.
A good 2CV is a magical thing!