Hired a car when over two years ago and found the driving fine. A lot of the roads can be challenging, i.e steep with lots of hairpins but once you get used it you'll be fine. As Tonyco1 says be prepared for a bit of reversing when you encounter buses and trucks as they are bigger than you.
Found Corfu Town ok to drive in but coming from the nightmare city of Edinburgh(in driving terms)
anything should be easy! There's quite a bit of parking up by the Old Fortress, close to the Liston and offering easy access to the narrow streets of the old town. Quite easy to find too.
Get a good map as road signage can be haphazard, particularly if driving away from San Stef. Coming out of Corfu signs were much more obvious. Also watch out for the road suddenly deteriorating with no warning and there are a lot of large potholes(just like Edinburgh too). Generally you are not covered for any tyre or underside damage. You're also likely to encounter donkeys and other animals in the middle of the road in the hill villages. And yes, watch out for speed traps.
Driving on the island is on the whole a great experience and is undoubtedly the best way to see and enjoy the spectacular views. Enjoy!