I believe the "deadpan atmosphere" David detected is actually Landis' complete lack of interest in the film.
It's really horrible. The 90's were a very rough time for Mr. Landis. A comedy director is only as good as his scripts, and the best in the world couldn't have spun gold out of the shit that were the scripts for Beverly Hills Cop 3, Oscar or Innocent Blood. Innocent Blood in particular has a dreadful script, torn between a lame mafia comedy and a lame horror comedy. The premise of a vampire mafia is pretty promising, but it goes nowhere with it. The only two moments that are worth your time are a delightful mortuary scene (with Frank Oz as the coroner) and Don Rickle's death scene. The make-up and effects for Don Rickle's demise are truly spectacular, where sunlight touches his body and he sizzles and fries like cooking steak.