Hi Jim,
Yes, you're right. GPS Datum should be set to WGS84 - the only exeption, if you use a GPS receiver with custom/other coordinate system uploaded (very rare case). Anyway, this is a common problem, heaps of customers make the same mistake. ArcPad converts WGS coordinates to your desired system on-the-fly (based on your file's projection) by default.
What you can do to resolve this with your mis-set files (if it's a shapefile):
Using Catalog, right click on the file and select Properties. Go to XY Coordinate Sytem tab and press Select button.
In Browse... dialog, select Geographic Coordinate Systems/World/WGS 1984.prj than press OK to apply. Your data should be ok now. Before you start to process these data, go to field and check OR compare this corrected file with a reference (basemap or other) to make sure the coordinates are okay.
Hope this helps.