Other mistake: In the flashback that shows Adam Brenner playing his opponent using the word "Exvin", we can see that the X is also used in "Juxtapose". When the opponent adds an S to "Exvin", he is challenged and made to take back his tiles. However, the X would remain where it is because it is a part of another word. Since the opponent plays a word using an X later in the game ("Loxodrome"), we know that he must have taken back the X as well. However, that cannot be the case as then "Juxtapose" would not be able to stand without the X. He couldn't play it as part of "Exvin" due to the existence of the word Antothenics underneath Juxtapose.
Suggested correction: I think they were implying that he played a second ex and that's what prompted them to look to see which tiles were missing from the suspects game. Since there were two x's used in the game and there's only X in each set it implies they thought someone was bringing tiles in from another set, and then they looked at the suspect set to see if any tiles were missing.