Hello Tracy and welcome to the forum !
That is a very loaded question and it has to be stated that any car from any brand can go wrong and do all have some issues from the outset.
What we can do here is try to show you the most common things to look out for when purchasing the lovely RCZ.
A little more info would have been good, do you want diesel or petrol, automatic or manual?
The MK1 petrol did have some teething problems mainly with timing chain and weak tensioner, this was quickly found and Peugeot did repair this issue under warranty several years ago. The MK2 hasn't seemed to suffer from the same problem, though out of the thousands sold an odd one has said had chain issue, but this could have been tensioner etc.
Other problems mechanical were issues with the coolant sensors - again these should have been fixed though some cars still have issues in this area, but they are reasonably easy fixes now.
The top model the R has had issues with the discs - again if a claim has been made whilst under Pugs warranty - these have been covered, again it was not all cars - just some of the R's.
Another fairly common thing to look out for is the high pressure fuel pump, this has varying lifespans !
Those are mechanical, but a problem which has been caused by the garages using incorrect lifting techniques, has resulted in the jacking points on some cars being bent over, hard to see from above, you have to get on your hands and knees, there is a tab that points down under the sills front and back, and it is this that sometimes gets bent from improper use as stated - this is not a fault of the car.
The most reliable by far with the least problems, is the diesel, it's engine is nearly bullet proof and it has good mpg too.
Have a good test drive and try a couple of different ones, there are plenty out there. If you can make sure you test drive the car from cold, if the dealer has warmed the car for you it could be to hide a noise or something from cold. Check the usual things and remember those jacking points, you might get some money knocked off or have them repaired before you buy. As with any car check all the functions if you can ie heating - hot and cold / a/c, try the spoiler see if it rises and falls as should, check clutch, you can give this a test and try set off in second, this could show a failing clutch. Check for any unusual noises and also check the dashboard for any warning messages. If you know someone with an OBD diagnostic kit , ask the seller if they mind you checking the car for faults, a good OBD reader will show any fault codes.
But mainly these are true for any car, so don't be put off by this list, I am just trying to be comprehensive with the checks. If you like it and it performs well without any issues, then they're probably aren't any, but if you are unsure - walk away, as said there is a good selection of secondhand Z's to choose from.
Sensibly and power wise, the GT200 is a good all rounder, but don't be put off by the marginally less powerful 156hp if you find one well specked and in good condition as you can quite easily get it uprated to very near the 200hp. The R is another story all together and if you can afford one and it's what you like, then go for it.
Options wise the Xenons seem to be the best one to go for, you can tell this if the car has headlight washers, then it will have Xenons as it is law for Xenons to have washers. Other packs are sports / black etc, but its what do you want, Sat-nav / JBL / leather heated seats ? it's upto you from here...
So, good luck with your shopping, it's one form of shopping that for some reason I don't mind LOL !!! :eusa-whistle:
Whatever one you buy, I am sure you will love it, it is the most sexiest car on the road in it's price bracket - end off !
Cheers M... :beer: