Visible crew/equipment: In the shot where the camera examines the hole in the wall and car made by Burt shooting the shrieker. You can see the shadow of the cameraman on the wall and his reflection on the car (near the top right corner).
Visible crew/equipment: When Bert is hiding in the tractor bucket you can see someone waving around the tongue of the monster. (01:19:27)
Visible crew/equipment: When the Shriekers are trying to find Burt in the front loader with their tongues, as the camera pans it catches the arm of a puppet actor in front of the front loader controlling the tongue. (01:18:00)
Visible crew/equipment: When Ortega introduces Kate to Earl and Grady, she turns from looking at Ortega to the others, and we can see the lighting rig reflected on her sunglasses.
Answer: It's a 50 caliber Grizzly Big Bore rifle. They are real. Just put "Grizzly .50 Big Bore" into your search engine and you will find plenty of sites.
Grumpy Scot