At Joe's Stone Crab, when Henry Desalvo is talks to Bruce and friends about cigar smoke and manners, he calls his steak "a great New York strip." In the previous scene, the steak on his plate was either a T-bone or a Porterhouse.
When Puggy is at the bar, eating Fritos and drinking beer, the bartender puts the money right next to his arm. When Snake walks in, the money is about 8 inches from Puggy. When Snake takes the money, it is right next to Puggy again.
When Snake shoots at Eliot and Anna through the gate window, he shoots only the top window out. When Eliot runs out to catch the plane, he leaves though the bottom window, which is supposed to be intact.
After Elliot chases the plane, Anna Herk runs to her right to get help. The plane starts taxiing to her left. When she sees Matt, and he asks where his father is, she points out the window, and the plane is taxiing by the window with Elliot chasing it. The plane should be nowhere near the window she points out.
The two F-16s fly with their gear down. When scrambled, an F-16 pilot will retract his gear as soon as the plane is airborne. This is not an error. Jet aircraft fly much faster than the turboprop passenger plane. In order to stay behind the plane, they would be configured to fly as slowly as possible, thus lowering the landing gear to increase drag.
The goof items below may give away important plot points.
When Snake holds on to the suitcase dangling from the plane, his gun is in his left hand, with his wrist hooked around the stair railing. The gun disappears briefly, then reappears in his left hand, hooked around the railing as before.
Undersea nuclear explosions produce "cauliflower clouds," not mushroom clouds. Mushrooms are caused by air being drawn up in to the fireball then cooling, causing a cap. Cauliflowers are caused by boiling seawater turning to steam and displacing the water around it.