In the scene when "Wild Bill" Wharton urinates on Terwilliger's leg and Edgecombe and Brutal are getting ready to throw him in the restraint room, Wharton takes his belt off getting ready for a fight. Death row prisoners wouldn't be provided with a belt for the same reason they wear slippers without laces; so they can't use it to hang themselves.
Nowadays it is customary (though not ALWAYS mandated) to take away belts & shoelaces from prisoners. Death row inmates, exceedingly violent offenders, and prisoners on suicide watch are usually treated more strictly with regards to these items. However, these rules vary from state to state, and most of them did not come into common practice until the 1970's or later (there have actually been cases into the 1990's which revealed lax or even non-existent policies regarding belts & shoelaces for prisoners). Since the movie is set in the 1930's, and in the south, it's HIGHLY likely that prisoners were allowed to wear belts (though probably not allowed belt buckles that were large enough to be used as a weapon).
Nomad762, I agree with your explanation to this slip; I also agree it's a minor slip. I'm judging this mistake on the book where the author explains about the shoelaces.