For all the people having trouble with their Nexus there are a few questions I like to ask.
1. Have you done a factory reset with Google backup turned off? Reason I ask this is because you could have corrupted cache backed up which will ALWAYS cause problems no matter what Android device you have. If an app is not 4.0 ready and you have it's cache saved it also may cause problems.
2. Have you tried flashing 4.0.2 again from Google Source? Reason for this one. Like with any computer sometimes things don't install right. Doing this may install the update correct.
3. Can I have screenshots or state what hardware version you have? Please remove any identifying lines if they are there like IMEI or telephone number. I have a theory and I want to talk it over with some coworkers to see if we can help.