The only problem, if it can be called that, I had with FF12 was that it was slow to load. Never noticed any problems with and web sites.
Ff13 is irritating me already though. If I open a new tab, it shows a page with a lot of boxes, presumably for favourite sites, on it, and it persists in putting the Welcome to Firefox one there no matter how many times I delete it. What on earth is wrong with a blank page for a new tab ?