From 1962 to 1972, the USA did actually field a Mk 28 'hydrogen bomb', later called B28, and there existed a B28FI version as the label says in Malory's presentation. However, its casing and tail fin assembly looked completely different; the picture in the presentation looks more like the 'Little Boy' bomb the U.S. dropped on Hiroshima in WWII.
Helicopters have two controls, throttle and cyclic, but the pilot of the Chinook helicopter is shown with both hands on a single joystick.
When Archer takes out his knife to 'trache' Pam, Mallory asks him "Since when do you carry a switchblade?" The knife, in fact, is a stiletto, not a switchblade.