Liam Neeson, Pamela Anderson in Comedy Reboot

The three-man comedy factory that ruled the 1980s with their fusillades of slapstick, sight gags, loopy non sequiturs and winking innuendo was David Zucker, Jim Abrahams and Jerry Zucker — Hollywood’s ZAZ before David Zaslav. Their legacy rivals that of Mel Brooks in the ’60s and ’70s, most notably via Airplane! and the Naked Gun movies, though I also have a soft spot for their swerve into more conventional farce with the acerbic dark comedy Ruthless People. Even the misstep of Top Secret! yielded its share of laughs, despite attempting to hit an unwieldy jumble of parody targets.

Having honed their skills in a college sketch-comedy troupe, the trio’s strategy was to throw as many jokes per minute at the screen as possible, the sillier the better, ensuring that enough of them stuck to cushion the ones that missed the mark.

Their 1982 ABC series spoofing crime procedurals, Police Squad!, lasted just six episodes. But ZAZ resurrected the idea for the big screen in 1988 with The Naked Gun: From the Files of Police Squad! (these guys seldom met an exclamation point they didn’t love), which became a successful trilogy centering on Leslie Nielsen’s bumbling but oblivious Detective Sergeant Frank Drebin.

Cut to 31 years later …

Nobody could accuse director Akiva Schaffer (who, like ZAZ, hails from a comedy trio, The Lonely Island) and his co-writers or producer Seth MacFarlane of lacking affection for the material. That’s evident in the sweet homages to Nielsen and George Kennedy as Capt. Ed Hocken — O.J. Simpson not so much.

The filmmakers follow the formula to a T in this legacy sequel or reboot or whatever you want to call it, enlisting the sons of Dreben (Liam Neeson) and Hocken (Paul Walter Hauser) as the new Police Squad team to provide plot continuity. Even if the movie kind of stalls midway as Schaffer struggles to balance the gags with the action of an overly elaborate crime plot, there are enough laugh-out-loud moments to keep nostalgic fans of the earlier films happy and maybe make some new converts.

Just as Nielsen was established primarily as a dramatic actor before becoming a ZAZ linchpin in Airplane! and The Naked Gun, Neeson arrives trailing the gravitas of his late-career reinvention as a steely dispenser of vengeance and retribution, in Taken et al. The actor’s dead serious delivery provides a subtle meta underlay as Frank Jr. takes down bad guys and tackles a master criminal, starting with a bank robbery prologue whose funniest jokes are given away in the trailer.

The heist ties into the suspicious death of a brilliant tech engineer, whose electric vehicle went off the road. The victim’s sister, Beth Davenport (MVP Pamela Anderson), seeks Frank’s help in investigating what she’s convinced was murder. He tells her to leave the detective work to the professionals, but they both turn up at a club run by her brother’s boss, Edentech founder Richard Kane (Danny Huston).

A mogul cut from the Elon Musk mold, Kane has a nefarious plan involving an amusingly named PLOT Device (Primordial Law of Toughness) with mind-altering properties, which is part of what he calls “Project Inferno.” But before that gets activated, he cozies up to Frank with the gift of Police Squad’s first electric cop car.

Weary of dealing with angry calls from the mayor about Frank’s blithe trail of city property destruction, police chief Davis (CCH Pounder) warns him to play nice with major donor Kane, since Police Squad’s funding is at risk.

That thread doesn’t really go anywhere in the script by Dan Gregor, Doug Maud and Schaffer. Nor does Kane’s talk of a “Doomsday Giggle Bunker,” where entertainment will be provided by “Weird Al” Yankovic — one of a handful of celebrity cameos. The same goes for Hauser’s thankless role as Ed Hocken Jr., who plays straight man to Frank’s self-serious dimwit, when the writers remember to include him.

Even in a spoof of a police procedural, the crime under investigation needs a minimum of internal logic, but mastermind Kane’s big scheme to destroy and remake Los Angeles — and possibly the world — to his own specifications pushes the movie almost into the absurdist espionage territory of the Austin Powers series. Senior or junior, Frank Drebin is an L.A. city cop, not Ethan Hunt.

Luckily, Neeson and Anderson have enough spark to carry the film, not to mention great chemistry. I could have done without the padding of a winter cabin romantic interlude with a killer snowman — there’s a difference between dumb and annoyingly stupid — but their scenes together are the high points throughout.

Hearing Neeson express Frank’s enduring anger about the Janet Jackson Super Bowl incident, reflect on the cultural importance of the Black Eyed Peas, berate Beth for messing up his Buffy the Vampire Slayer recordings or break down the characters on Sex and the City after someone says “Miranda rights” is a droll pleasure. His tough-guy physical comedy also scores, as he swats off armed criminals or bites off the barrel of a gun pointed at him without breaking a sweat.

There’s a moment early on in which he kneels beneath his father’s photograph on the Police Squad wall of honor and says, “I want to be just like you, but at the same time, completely different.” Which is pretty much the manifesto of anyone reviving a popular franchise after multiple decades of dormancy. The Naked Gun is at least a step up from the lifeless Beverly Hills Cop: Axel F, to name one recent example.

Neeson clearly is having a blast sending up his hyperviolent screen persona of recent years, and his enjoyment is infectious up to a point. But even when the narrative momentum sputters as the movie loads up on jokes at the expense of structure or character, Neeson’s scenes with Anderson are bliss.

Continuing her renaissance after The Last Showgirl, Anderson displays impeccable comic timing, never leaning too hard into a line when her breathy throwaway delivery can land a bigger laugh. At one point, Kane asks Beth, “May I speak freely?” She replies, “I prefer English.” In another moment, Frank, curious about where she went to college, asks, “UCLA?” With only the tiniest frown of confusion, she tells him, “I see it every day. I live here.”

Dialogue like that may come from the hoariest school of comedy writing, but the charm of Anderson’s buoyant screen presence keeps it fresh and funny. Beth is a character who defends her crime-solving instincts by saying, “I write true crime stories, based on fictional crimes that I make up.” But it’s crucial to Anderson’s performance that Beth sails over every idiocy the script throws at her as if she’s making perfect sense.

I kept wishing the movie were as consistently entertaining and as sure of its footing as Anderson and Neeson are in their roles. But even if the laughs are hit-or-miss and the plotting shaky, there’s enough inspired nonsense here to keep comedy-starved theatrical audiences engaged. To the filmmakers’ credit, that includes the kind of retrograde, politically incorrect humor — the cops’ anatomical appreciations of Beth are a hoot — that makes the movie feel almost like the old Naked Gun.