Revealing mistake: When Burt returns after being ambushed by Graboids, Grady is holding a rifle across his shoulder. He has two fingers in the trigger guard where there should be a trigger. You can see it has no trigger. (01:06:29)
Revealing mistake: It's very clear they blew up a model of the buildings. The grass seen just before the explosions is way too long and is not as long when the characters are running away. Further, the truck and the barrels have disappeared at the explosion shot.
Revealing mistake: When Grady & Earl blow up their first graboid, one of the pieces of orange goo that hits the truck flies in from the LEFT. All the other pieces of orange goo get flung in from the right.
Revealing mistake: When they are using the broomstick in front of the Shrieker, there is a seismometer in the background. At the very start of the scene, the screen reads "Kathy's Lab Template," and then the screen flickers before showing the seismometer as normal. This indicates that this is just playing back from a pre-recorded VHS tape.
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