The character, Dave Barrett, wasn't really a private investigator. He was - as the show's title infers - a "manhunter", a bounty hunter. Dave returned home, a WWI veteran, to find his family is having a hard time making ends meet due to the Great Depression.
Dave decides to supplement the family's income by collecting the bounties on the Dillinger-esquire gangsters that were prevalent (apparently *very* prevalent in Kansas - who knew?) in those days.
So Dave fixes a car up with hiding spots for some of his war souvenirs (seriously, a Colt .45 auto and a Thompson submachine gun - plus a bayonet, a shotgun, and a Winchester rifle! Dog could take lessons from this guy.) and set off each week to earn some extra milk and egg money.
Maybe it wasn't quite historically accurate; but it was a fun show.