Is this a plot hole in the fake test scene in the first episode of Charlotte?
Rewatched the first episode and I can definitely say that there is no plothole, at least to the incident you were referring to.

In Episode 1, when Yū took the test, the unnamed student council president was supervising him. Yū possessing him has no effect as the unnamed student council president has no power at all. To clarify, it was not Jōjirō who was watching over him while taking the test.

Furthermore, during the episode, he never possessed Jōjirō so no, there was no way he could have stolen Jōjirō's power. 

By the way, Jōjirō's power is not teleportation but rather, 


  the ability to charge at extremely high speeds in one direction.