I have a similar problem. I have a 3G that was running 4.0 until yesterday, when I jailbroke it using a popular online tool (that I'm not sure I can name

).
I had an App Store-bought app on my phone beforehand that records audio (iPodcaStudio), and due to a bug it can't delete clips, so I deleted it off the phone and attempted to resync the app back after backing up the clips. I can't, however, sync this app back to the phone.
When I plug my phone into my computer, the app sync tab has the icons for everything that is currently on the phone but a blank white App Store icon for everything that isn't. Even though the iPodcaStudio app is checked, it won't transfer to my phone.
I had FiveIconDock installed but removed it after reading above it may be the problem. I have also tried to sync in Safe Mode with no success. I'm about to uninstall and reinstall iTunes but if anyone has any help it would be appreciated.
I'm running Windows 7 Ultimate and iTunes 9.2.1.5 if it helps.
EDIT: Okay, this may not be an issue with the jailbreak itself. I transferred my iTunes library between computers a while ago and may not hav transferred the apps - it looks like all the ones with the white squares are ones I downloaded before the transfer. To test, I'll delete one I've added post-transfer and see if it syncs.
EDIT: Yeah, this isn't a JB issue. All my apps were in the wrong folder. Sorted now.