Cooker certification?

No.

For big 'uns like Southern Pride, Cookshack, etc. you'd need UL approval for the wiring - I know the FEC500 and FEC750 are NSF and UL approved.

Most other cookers have not been offered up for inspection - both UL and NSF are voluntary...though well worth it for the commercial builders that expect their equipment to be used "indoors".

Clean would be the main consideration - assuming an inspector ever tracked you down.

Chad hit it on the nose. NSF certification is not mandatory. Sure makes the inspector easier to deal with though.

I'm sure I posted on this subject somewhere.
But our health inspector is primarily designated to the inside of the building.
I could probably cook in a shopping cart, and much wouldn't be said.
The only thing AZ law says about outdoor cooking is that it can't be served outdoors directly from a grill or smoker.
It has to be brought inside to be served, then the individual can take it outside and eat it if they want.