This Workaround definitively workded with several iDevices (iPhone 4, iPhone 3GS and iPod Touch)
It solved Batterie, WiFi, 3G and GPS issues, which occurred after updating the device (also to 4.3.3)
0. Sync your Contacts and Calendar to anything compatible to iDevice (smth different than iTunes, Outlook, Google or smth else)
1. Restore your device in iTunes, but don't activate it (that iTunes doesn't apply any changes to it) just disconnect your device when iTunes claims about SIM-Card
2. Uninstall iTunes completely (preserve your iTunes Media Library)
3. Add a new Admin user to your OS
4. Login as new Admin user (you created in step 3)
5. Install iTunes
6. Set your device to DFU mode (- Power off device, - press Power button for 3 sec, - press home button for 10 sec still holding Power button, - release Power button continuing holding home button, - release home button after 20 sec).
7. Connect your device to PC/MAC
8. Wait for iTunes starting or start it manually
9. Restore your device in iTunes (let iTunes to download the FW again, don't use old file, just to be sure)
10. Activate your iDevice
11. nJoy!
PS.: I didn't try to restore my Phone from old backup after this procedure. I don't know if your device then will still work fine. You may whant to do so, then you can post here if the old issues'll come back (I suspect they will). But you can still use your old iTunes Media Library and restore your Contacts and Calendar from where your synchronized it in step 0.
All iDevices I restored this way, work with newest FWs already for more than a week without any issues.