The CBR600F and its slightly sportier brother the F-Sport (which gains a lighter flywheel, dual valve springs, a split seat and no centrestand) are two incredibly rugged bikes and mechanically are virtually faultless. That said, you do need to keep an eye out for a few small issues…
All Hondas from the 1990s and 2000s suffer from cam chain tensioner issues. The problem starts as a rattle when the bike is cold, which is when you need to nip the issue in the bud before it get considerably more serious. Swapping the tensioner isn’t a massive job, or very expensive at under £100, but it is a fiddle with the tensioner tucked away in a fairly annoying location. Some owners swear by manual tensioners, but these can lead to more issues – stick with an OE Honda unit.
The reg/recs on CBR models can cause problems, but they aren’t too expensive to replace, and most times it is the reg/rec and not the generator that is at fault – a considerably easier and cheaper unit to swap. And don’t worry about the red ‘master’ key for the HISS immobiliser system, unlike Yamaha models the Honda doesn’t have one!
When it comes to buying a CBR the best advice is to use your eyes. If the bike looks like a hack then it probably is one.