One problem related to differential unit has been reported for the 1997 Ford F-350. The most recently reported issues are listed below.
The planetary gear failed while driving. It completely discentrated inside the transmission. A local Ford dealer rebuilt transmission, but now, when the truck is warmed up and the transmission is hot, when you engage reverse it takes off on its own. I have to hold it back with the brake and it eventually stalls. This has happened repeatedly.