Throughout the series, Atlantis standard procedure seems to be for team members to remove insignia and nationality patches from their jackets when off-world. When the team meets the abbot in the village, Sheppard is still wearing his jacket patches, though they are removed in a subsequent scene.
Dr. Grodin says he has been working on deciphering the Ancients' logarithms to determine the function of a piece of equipment. Logarithms (mathematical functions that are the inverses of exponential functions) would be useless and not require a lot of "deciphering". Presumably, he meant the Ancients' algorithms. Dr. McKay should have known this, as well.