A 5 kiloton nuke, while damaging to the city of Las Vegas, would only destroy a few city blocks, hardly the "destroy the city" level threat that they state it to be.
C. Thomas Howell's character, Haggerty, is supposed to be missing a right thumb. You can clearly see that in Episode 1 "Real American Heroes" at the 17 minutes 5 seconds mark that his right thumb is intact.
At 00:01:48, the terrorist puts an alligator clip on an insulated wire making it impossible to have electrical contact.
No one in any branch of the U.S. military introduces themselves as "This is the United States Military".