Right now Trimble is working on the new version of GPSCorrect that will work with ArcPad 10.
The latest GPSCorrect is Version 3.13. It can be used with ArcPad 8.
Unfortunately 3.02 will not work with ArcPad 10. As Rui mentioned above, Trimble is in the process of releasing a version of GPScorrect that is compatible with ArcPad 10. Therefore the next and newest version will also be the oldest version compatible with ArcPad 10.
You can always check the software compatibility. There's a pdf (some 28 pages) on Trimble's website which they regularly update, called Mapping & GIS Product Compatibility List. You can search for it, or use this link to access. Last update: 5th August, 2010. (Or ask your Trimble Dealer to send it to you.)
Hope this helps
Trimble announced today that they have released a new version of GPScorrect and GPS Analyst that works with ArcPad 10.
I have question though, do you need the newest version of Analyst or Pathfinder to post-process the data collected with this new GPScorrect on ArcPad 10?