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: I did not see this episode, but YES. Both prosecution and defense lawyers use investigators to search for and uncover evidence that is legally admissible.