Sven, Kirk,
I've just finished a clean install of Mountain Lion on my MacBook Pro. This included a clean install of PM5 and the service "browse with PM." I can now fully describe the issue at hand as well as the workaround/solution.
Issue is simply that out of the box, the "Browse with PM" service does not work even though it shows up as an option in the Finder. I'm pretty sure it is because the service is referring to the wrong path for the application. Kirk, if this is indeed the case, I think you guys should be able to solve this easily.
Awaiting that more permanent fix, this is how you solve it yourself: open the contextual menu in the finder and instead of normal clicking, hold the alt key while clicking the "Browse with PM" option. This will present you with a dialogue box asking you to locate your version of PM. Select the application, and all should work again.
Hope this helps,
Hayo