Why does TitaniumBackup not allow me to restore apps after upgrading to 4.3? After upgrading to 4.3 from a previous version (in my case 4.2), TitaniumBackup might exhibit a behavior where restoring apps does not work and the process just freezes on some devices, in this case a Galaxy Nexus phone. It seems that restoring app settings might work, but when restoring the actual apps this triggers the freeze. Restoring XML data like Wi-Fi hot spots also works.
To fix this issue, set TitaniumBackup to use the legacy path. The easiest way to do this is to go into TitaniumBackup, press "Menu" and then "Preferences". "Backup folder location" a bit down and click it. Click "DETECT!" and TitaniumBackup will ask you where to scan for backup locations. It's very important that you here choose to scan your whole device and not just the SD card.

After scanning is complete, you might as in my case see that TitaniumBackup presents two paths that seem almost identical (in fact they sort of are). Choose the path that has the string /legacy/ in it, in my case it is /storage/emulated/legacy/TitaniumBackup — which should replace a path similar to /storage/emulated/0/TitaniumBackup.

After TitaniumBackup has been reconfigured to use the legacy path, restoring apps will work as normal. Thanks to necropuppy for this solution.