The cut that Dr. Mittenhand puts on Tina's thigh is viable before he attacks her. In fact it is first seen when her pants are taken off her in the crawlspace.
Kowalski refers to himself as a "Marine". He frequently calls MSGT Hooker "Sarge". "Sarge" is strictly an Army term - a Marine would call a Master Sergeant either "Master Sergeant" or "Top".
Characters are seen smoking in a spaceship in spite of the concentrated, pressurized oxygen inside it (since without it they'd be dead because space does not have oxygen).
When Dr. Mittenhand is trying to fix his computer by slamming his fist against it, you can briefly see his other "missing" hand behind his back.
At one point in the movie, the leprechaun seems to either fly or jump really far across the screen. As he does so, the thick cable attached to him is visible.
When the Leprechaun comes out of the soldier's body and then shoots from another angle, you can see that the Leprechaun comes out from a hole in the ground.
At around 13 minutes, when the Leprechaun kills the marine with the light saber, the blood is on the ground before his head touches it.