Visible crew/equipment: When the Shriekers are trying to find Burt in the front loader (tractor with bucket) with their tongues, as the camera pans it catches the arm of a puppeteer controlling the tongue, in front of the front loader. (01:18:00)
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: After Burt shoots a hole through the wall, the camera shows the hole and backs up. Its shadow is on the right of the screen.
Visible crew/equipment: Right after the Graboid jumps onto Earl's truck, they panic and reverse really fast. There is a shot looking through the back window of the truck. The camera reflection is fairly obvious.
Visible crew/equipment: When Burt shoots at the Shrieker with the high-powered rifle, a frame of two before the Shrieker explodes, a wire is visible at the tip of its beak, holding it up. (01:16:45)
Visible crew/equipment: When Burt Gummer is shooting at the Shrieker, in the top left corner of the window you can see a crewmember quickly bash the window causing it to shatter.
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