At 31:35, as Col. O'Neill runs around searching for Maybourne, he runs into what looks to be a haystack and knocks over a metal pitcher. In the very next shot, the pitcher has returned to its original position.
The large moon visible in the sky over the planet is blended in erroneously: no stellar object, seen through an atmosphere, can appear as darker at any point than its void background.
When O'Neill uses his beer to put out the fire on the paper, it is clear the Guinness is really water.
O'Neill and Maybourne are stranded on the moon for over a month with limited supplies, but O'Neill remains clean shaven for most of that time.
Several different times Carter, and others, address Maybourne as "Colonel", which is completely improper. Following his court martial and conviction of high treason Maybourne was stripped of his rank and dishonorably discharged from the Air Force. He no longer deserves the title of Colonel and it is highly improper for other military personnel to address him by his former rank.