There are several references to the "Thai Federal Police", there is no such force. The correct term is "Royal Thai Police".
When sharing trivia, Vincent makes two mistakes. First, he says that Speaker of the House is not allowed to speak, which is a far stretch, as the Speaker is not considered an apolitical public official and thus simply cannot make political statements. Second, he says that it is impossible to lick one's own elbow. This is by all means possible, as many contortionists have proven over time. It is also quite easy, yet painful, after one dislocates a shoulder joint.
(at around 1 min) The hip bones of the skeleton lying on the table are upside down.
Just before the 30 minute mark, Sweets proposes a bet with Booth, who accepts. The series has established that Booth is a recovering gambling addict multiple times. Booth's chip is even seen in this episode. As his psychologist, Sweets would never bet with a recovering gambling addict.
When attempting to identify the victim as a transexual, Dr. Saroyan states that the she had high levels of spironolactone in her system. Spiro is a testosterone blocker. As a post operative transexual, (i.e. no longer has testicles) she would have no need for a testosterone blocker.