Why does Reg Cure shut down, while scanning file path references?

It could be hitting a set of files that are in use. Does the log tell you any more about which file paths it was up to when it stops? you may need to set up the options to write you a log.

This is one reason why it is generally better to run all scanners in Safe Mode - a lot fewer programs and drivers are loaded, so a lot less is in use for the scannner to get stuck on. (Also some viruses can "hide" from a scanner in Normal mode, but in Safe mode there is a very high chance that the program they are attached to is not running, so the virus itself is also "asleep").

Many Registry "tweakers" will do strange things sometimes. Always back up your registry before running them.

For a simple (free) alternative, that gives YOU the choice of what to change or remove (with explanations), try using Regcleaner instead of Regcure

http://download.com/TweakNow-RegCleaner-