Plot hole: The resolution of the case hinges on the fact that the culprit would be compelled by The Witness (whom they bribed, but who double-crossed them) to visit their stake-out apartment to try to dispose of their bloodied clothes. However, The Witness didn't and couldn't possibly know about that apartment. The murderer tried to prevent a non-existent threat that nobody made and did not worry at all about the other, very much more likely evidence and testimony The Witness provides - if The Witness was going to trick them to begin with, it makes no sense that they didn't just record the conversation, for once. The culprit does not even contemplate that possibility.
Plot hole: Matlock figures out that The Professor wouldn't have been able to see the security guard from 50 yards without glasses, and that's what tips him off about The Conspiracy: the guard testifying that the man wasn't wearing any. However, when we see the scene happen at the beginning of the episode, the person posing as Prof. Erskine Tate is, in fact, wearing glasses. (00:04:15 - 00:22:15)
Plot hole: The forensics for this case have been quite shoddy at best, considering that Tate was drugged and not simply intoxicated (yet no toxicology test was performed) and the dog wasn't run over but repeatedly beaten with a tyre iron (which is a wildly different kind of injury). Nobody brings this sort of objection forward - the dog one would have easily destroyed the prosecution's case right away since The Professor was asleep at the wheel and not in shape to beat assault dogs up.
Answer: Leanne often went to the beach whenever she was upset about something. In this episode, Leanne realised that Kevin, the guy she had been seeing, had broken into her home and taken her diary in hopes of learning everything about her. This upset her because her privacy had been invaded and Kevin thought that the entries in her diary described the kind of man she was looking for. Ben drove down to the beach to comfort Leanne.
Only problem with that is that earlier in the episode LeeAnn went for a jog on the beach. She drives three hours to jog?
She didn't go for a jog. She went there because she was upset.