Returning Japanese (1) - S6-E21
Plot hole: In this episode, Hank meets his paternal half brother. They look alike. However, we saw in an earlier episode that Hank's facial structure takes after his mother, not his father. Since they are paternal half brothers, then the Japanese brother cannot look like Hank since he has a different mother.
Plot hole: Whenever Gretchin calls Mikey up to the stand to explain what he saw, he says that he had followed Spinelli and Randall to the wooden fence, where he Saw Randall on his knees in front of Spinelli, begging for forgiveness, then Mikey began running to the other side to stop Spinelli from pummeling Randall with the "rock" but didn't make it in time. We then later find out that Spinelli had actually rescued Ms. Finster's cat out of a tree and Randall hit himself with the rock out of spite. But it is impossible that Spinelli could have given up on hurting Randall, climbed up a tree, rescued a cat, climbed down, handed the cat back to Ms. Finster, gotten praise from Ms. Finster, then have Randall attempt to pick up a big rock, then get a smaller one and hit himself with it in under 3 seconds (the duration of how long Mikey ran before he heard Randall's scream).
Hida Mechanical Mansion Murder Case: File 3 - S1-E20
Plot hole: Even considering the fact that the corridor was dimly lit (but not in complete darkness), it is impossible to plan the 'switch' the way it happened. For the plan to work, the killer needed to go through a revolving door at the same time as Kindaichi; there was no guarantee which of the two halves of the door he'd make spin, though, and he needed precise timing (against someone running through the door at full speed) and not make a sound with the keys he was carrying. The corridor (and therefore the door) is also so narrow that you wouldn't be able to ever pull it off.
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.
The New Kid - S2-E7
Plot hole: In the season two episode 'The New Kid,' Daria and Jane are discussing The New Kid in gym class when a girl takes a nasty spill from a trampoline. Later, Daria and The New Kid are heard remarking about photos taken of that particular fall despite there having been no photographers present.