The most prominent weapon in the film, the Spectre M4 SMG is carried by Valkenvania Police Chief Constable Dennis Valkenheiser (John Candy), and used by Constable 'Miss Purdah' (Valri Bromfield). The Spectres in the film do not have foregrips nor the folding stocks.
An interesting note, the semiautomatic-only version of the Spectre has no foregrip or folding stock, like the weapons in the film. However, the Spectre fired by Miss Purdah in the film is fully-automatic. As such, these guns could very well be either full-auto versions that simply have the foregrips and folding stocks removed, or perhaps semi-auto versions (with the firing gun simply being one converted to full-auto).
Handguns
Smith & Wesson 639
What appears best to be a Smith & Wesson 639 pistol is carried by Miss Purdah in one of her dual reverse-draw holsters - Best seen in the larger shot of when she aims her CAR-15 alongside her vehicle.
Beretta 92FS Inox
The pistol in Miss Purdah's other holster best appears to be a Beretta 92FS Inox.
Walther PPK
Alvin Valkenheiser's (Dan Aykroyd) personal weapon appears to be a stainless Walther PPK pistol. Chris Thorne (Chevy Chase) very briefly handles this weapon. The PPK pistol in this film appears to have engraving on the slide and Ivory grips.
Colt Python
During a stop, an inebriated crook named Arthur (Daniel Baldwin) pulls a nickel-plated snub-nosed Colt Python on Dennis (John Candy), though it gets quickly knocked out of his hand. It is seen again a bit later on the desk of Judge Alvin Valkenheiser (Dan Aykroyd). A State Trooper at the end of the film also wields a full-sized blued-steel Python.
Beretta 92F
As Judge Alvin Valkenheiser examines the confiscated items, including the Colt Python Snub shown above, a Beretta 92F semi-auto pistol can be seen on the desk.
Rifles
CAR-15
The main weapon carried (though never actually fired) by Constable 'Miss Purdah' for a fair portion of the film is a CAR-15 rifle.
XM177E2
Interestingly enough, later in the film, Miss Purdah carries what appears to be an actual XM177E2 rifle, most likely standing in for the CAR-15 shown earlier. Like the CAR-15, it is never seen actually being fired, so it's likely this weapon may be a dummy gun or other non-firing prop. It is a very close looking example, in any case.
Ruger Mini-14 GB Stainless
Miss Purdah carries and fires a Ruger Mini-14 GB rifle with scope and stainless barrel/receiver later on in the film as she chases after Chris and Diane (Demi Moore).
M16A1
National Guardsmen accompanying the State Troopers are armed with M16A1 rifles with 20-round magazines.
Unknown Bolt-Action Rifle
A State Trooper takes position with a scoped bolt-action rifle of unknown Make/Model.
Shotguns
Mossberg 500AT
Towards the end of the film, some State Police Troopers carry what appear best to be standard Mossberg 500AT shotguns.