Plot hole: Throughout the series, auxiliary characters are always far too willing to give all kinds of information to Tru. Doctors and registrars constantly give her privileged information about patients and students. Tru is often able to retrieve information like addresses and phone numbers from people's service and utility companies, when normally you must verify your own information before they will even talk to you about your account. Of course there can't be an episode if Tru doesn't quickly find the person who asked for her help, even though she doesn't usually know much more than their name, but it's still a bit conspicuous.
What Is And What Should Never Be - S1-E20
Plot hole: How in the world could Keith be hired as a teacher? Not only is he a college drop-out with no teacher training, Dan mentions just an episode or two earlier how Keith is incapable of using modern machinery (specifically saying how every high school graduate will be more qualified than Keith).
Shrink Rap - S5-E2
Plot hole: The man plays his last nickel and wins the jackpot. You have to play the maximum number of coins to hit the huge jackpot which on that machine states is 5 coins.
Plot hole: People who do not have their souls retrieved, before they are killed, will suffer the effects of the death on their soul, eg. the autopsied man has scars and cuts on his soul. So how come the woman who was crushed by a piano (whose soul was only ever retrieved afterwards) is unharmed in soul form?
The New Era - S2-E4
Plot hole: Early in the episode, Alex tells Seth that the night of the Killers concert is her night off. (She works at The Bait Shop, the concert venue.) At the end of the episode, Alex is paying The Killers, as if she were the manager on duty.
Orpheus in the Undergrowth - S2-E2
Plot hole: When Jeremy stopped to drink his water, which turned out to be vodka and which killed him via a heart attack, why did he hide himself away, surrounded by plants and only found by his mobile ringing? And why would he put the lid back on the bottle in the throes of a heart attack?
Plot hole: Towards the end of the episode, Mr. Alderman ties up Cherry Peck and forces Matt to cut off Cherry's male genetalia. Matt does so, and Cherry screams in pain. Later on that night (probably at least an hour later in what would be "real time"), Mr. Alderman and Matt drive to a secluded area and Mr. Alderman forces Matt to bury Cherry alive. Matt refuses, and Cherry eventually steps out of the grave and strikes Mr. Alderman with a shovel before shooting him. Cherry has the same clothes on, but is in no sign of pain, or is even bloodied from the earlier trauma. It is safe to assume that neither Matt nor especially Mr. Alderman would have driven Cherry to any hospital, nor would any hospital even have let her out in an hour or two's time after an injury like that.