I don't have badge clear installed, but I'm getting the spring board crashes randomly when either I clear or open an app from Intelliscreen. No rhyme or reason as to which apps cause the issue either.
I'm an iPhone 5 using iOS 6.1. I installed the iOS fresh and restored the settings after.
It's ridiculous that they tell you to turn off every app in mobile substrate and then wait for the problem to occur. You would have to re-enable each app and wait, wait, wait till it happens again to hopefully determine which app is causing the issue.
How about putting some basic logging into the app that could be shared via email when the thing crashes like most other programs? Ridiculous that they didn't / don't do this especially with the amount they charge for the app. Pathetic really!