I downloaded Path Finder and like it a lot, but Finder still takes over some functionality that I'd prefer Path Finder to do. For instance, if I open a folder on my desktop it opens in Finder, and when I mount disk images, they open in Finder. Is there a way (short of going in low-level and replacing Finder stuff with Path Finder stuff, which I don't really want to do) to make Path Finder do everything that Finder does by default?
According to the Path Finder Support Forums, it is not possible to completely replace Finder with Path Finder. For more information see "Can I replace OS X's Finder with Path Finder?"
These days (2016) Path Finder is much better integrated already from the start. Often not having Finder running is a good prerequisite for having Path Finder take its place, but this is not always necessary. You can make Finder quit when Path Finder starts in the preferences (See the Finder tab) and you can quit Finder from there as well.
A convenient way to quit Finder is also adding a quit command to its Archive menu by typing this into Terminal
The following two techniques should make Path Finder take the view calls from third party applications, but "Show in Finder" when selected from the Dock will probably not work.
Setup Path Finder to intercept Finder calls
Make Path Finder default file viewer