They call the signature a 'double-knot ligature' where it ought to be a 'double-knot suture'.
It is stated that the "Silencer" used "six-zero nylon" to suture the mouths of his victims closed. The suture shown is much larger than 6-0 nylon, which is about as thick as three human hairs, and is only available on a tiny needle. The suture used was more likely #2 silk, which is thick, braided, black, and comes on a big "CTX" needle.
Paramedics don't do suturing, so there wouldn't have been suture kits in the ambulance.
The note in the victim's mouth says; "Gazing through to the other side." Reid says "there's no reference to it anywhere." Not true. The reference is to Blitzen Trapper's 2008 song "Black River Killer", which was the influence for the entire story.
In two separate scenes, the Unsub's birthday is shown on Garcia's screen as January 10, 1974 and October 1, 1974.
When the man that is supposed to be living in Sweetwater, TX pulls up to his house, small mountains can be seen in the background. Sweetwater is in very flat country, no mountains are in that part of Texas.
Blake says that the fact that the unsub knows IPA (International Phonetic Alphabet) is "proof" that he can hear. The word "proof" is too strong an assertion, and a scholar with as many academic credentials as Blake has would not use it in this fashion. Knowledge of IPA only proves knowledge of IPA (although it is a strong indicator of knowledge of speech sounds). Proof that an individual can hear in the absence of any behavioral indicators usually has to be done with some sort of other neurological audiological testing that is not dependent on behavioral measures.
As a seasoned FBI agent, JJ would have known better than to reach into a medical waste bag (that she found next to the baby's car seat by the tree) without gloves on. Especially because it was potential evidence and also medical waste.