I doubt it was a goof that was overlooked. It could be an intentional "gaffe" to emphasize his ineptness.
Also, there were some westerns where the gunslinger prefers reaching across his body for a less restricted "draw" and wears his guns backwards. No idea if that's a real thing, but definitely was intended for a certain amount of badass "cool," so it would also be an intentional thing where this somewhat inept officer wears his guns like that in a lame attempt to look cooler or tougher than he is.
Or, he wears it like that intentionally, for the reasons stated in the second paragraph, but because he actually prefers the draw motion across the body. Was his holster on the opposite side from his shooting hand?