That said, there are some alternatives to Cyanogenmod's Incognito mode, which should work better.
One is XPrivacy [2], which relies on the XPosed Framework [3]. This is what I'm currently using on my Android phone. You can allow/restrict some permissions by default, and then have a whitelist for certain applications.
Another one is OpenPDroid [4], which requires you to patch your rom (there are some preset for the biggest roms, so usually it's just a matter of a few clicks). I haven't used it, but it should work just like XPrivacy.
XPrivacy and OpenPDroid send blank/fake data instead of blocking applications from using certain APIs, so they cause way less crashes. They even allow you to choose the fake data to provide, so that you can fake, for example, your location.
[1] http://www.androidpolice.com/2013/07/25/app-ops-android-4-3s...
[2] https://github.com/M66B/XPrivacy
[3] http://forum.xda-developers.com/showthread.php?t=1574401
[4] http://forum.xda-developers.com/showthread.php?t=2098156