Is it a good idea to reinstall OS X to attempt to fix some minor issues? I am having a couple of problems with my Mac (wifi doesn't connect automatically, and audio jack doesn't work unless I restart).

Having failed at fixing them for a while, I am wondering if reinstalling the OS (Mavericks) might help in such a scenario and should be given a try? (Obviously, I want to reinstall while keeping all my data, settings, apps etc intact.)
Yes, a variety of strange software problems can be fixed by reinstalling OS X. Providing the installer detects an existing install (which will only not happen if the disk can't boot) your files and settings will be preserved. If you've made any changes to the system such as modifying a keyboard layout or changing the boot logo, you will need to back these up as they will be wiped.