Plot hole: During Ryder's report, as Bruce and company watch it on TV, the camera suddenly zooms in on Joker standing on a catwalk above Ryder, and none of the crew, especially not the camera man who caught the villain, makes a comment about this. They may have thought the Joker (or rather an impersonator) was perhaps a surprise gag in the show, but since this is supposed to be a serious documentary report, it is still strange that they wouldn't point it out.
Plot hole: The whole episode is based on false facts. Cody was getting an A in woodwork and Zack was failing in all his classes the previous year at school (according to their report cards in Ep "Smarter and Smarter"). So Cody knows a lot more about woodwork than Zack and should be able to make a clock, never mind a birdhouse, and Zack should not be able to make a clock.
Plot hole: The Jupiter 2 crew is duplicated; however, the aliens had never seen Penny (or Judy I think). How can they be duplicated? The aliens don't have ability to know who were there, or they wouldn't have questioned Smith about the crew. Also, they do not know Smith and Will are hiding. So, they don't arm to have any special power to know beyond what they actually observe.
Plot hole: When Danny Kendall first appears in series 9 (1986) he is in the third year, then the fourth year in series 10 (1987) but in series 11 (1988) he is put down a year to help him catch up with work he missed as he was in hospital for most of his fourth year. But in series 12 (1989) he is in the fifth year when he would be aged sixteen going on seventeen and he would not be legally obliged to stay on at school, as sixteen was the legal school leaving age then. When Danny died in series 12 the school planted a tree in his memory with a plaque in front of it giving his birth date as 8th January 1973 and death date as 22nd January 1989. His birth date should have been 8th January 1972, as he would have been seventeen years old when he died.
Into the Mouth of Evil - S2-E23
Plot hole: While fleeing the guru's disciples through a narrow side street, Jackie gets cut off by the van driven by Dr. Jamba and associates, stun-sprayed in the face, and then loaded into the van. But with three brutish-looking guys being so close to their quarry, the real crooks can take the time for dragging Jackie around to the back door instead of loading him through the side doors?
Plot hole: Why would Danger Mouse go on the roller coaster at the end without seeing Greenback go on it first? Greenback went first in the ghost train. It also doesn't make sense that Danger Mouse would go on it when Penfold pretty much tells him flat out that it IS a trap.
Plot hole: Tim has the mike in his hand and steps repeatedly forwards to talk to Jill, the cord being long enough to allow him to do so. However once Jill leaves and he wants to go after her the mike knocks over the jar of mosquitoes. Up until then, there was no indication that the mike had been changed or moved but he never at the risk of knocking over the jar until then.