Battlestar Galactica (1978)

Continuity: When Baltar turns to face the two setting suns, we see the lower one at the left has what could be a boat in its reflection on the water. The higher one on the right is over a mountainous area on the horizon. The next shot is of Baltar in close-up, then the next returns to the horizon to show us Baltar's view, which shows just ONE setting sun. The one on the left has vanished though there is room enough for it to have been seen in this shot.

Continuity: When the Warriors are playing cards, Starbuck places his cards on the table near the gold coins, saying "A perfect pyramid. Unless there's a better hand, the pot is mine". His right fingers tap on the table and his cigar is in the ashtray. When the shot cuts, his hand is suddenly up by his mouth, holding the cigar, and the cards and coins have vanished.

Continuity: When Apollo and Boomer enter the club, Apollo walks in, placing himself near some curtains while Boomer walks ahead. When the shot cuts, Boomer is suddenly standing right behind Apollo.

The pilot crests (worn by Richard Hatch and Dirk Benedict, among others) on their collars were actually U.S. Army Military Intelligence Class A uniform crests.

The patch worn on the Rising Star medical uniforms is actually the shield for the United States Air Force Academy.

Episode 18 - "Baltar's Escape": This is likely a mistake, but it's a self-excusing one that, if intentional, was a nice bit of inspired continuity. In "The Man with Nine Lives", a Colonial Warrior, played by an actor not seen previously, is guarding new recruits that are confined in their quarters awaiting security clearance. He not only freely gives out classified information, but is eventually overpowered by two phony recruits and locked in a supply closet. Then, in "Baltar's Escape", the same actor appears as a member of the Council of 12's security team. It's likely the film makers thought no one would recognize him, but given the disdain that Colonial warriors have for the Council's security people, it is fitting to see this failed Warrior reassigned to the Council - a nice touch, even if not intentional.