The message consisting of three glyphs written in a row has two errors.
1) Ancient Mayan was written in columns consisting of two characters side by side, not three in a row.
2) Each character represented either ONE word or a phonetic sound in an alphabet, so the three characters in the note would be THREE words not the long complex message that is reported.
The "gargoyle" is actually a grotesque, as gargoyles traditionally were waterspouts carved into the shape of a creature.
The body was mummified and yet Lainie confidently proclaims she knows the girl was killed 4 months ago, which is impossible to determine on a mummified body since all the internal organs would have been removed and the remains desiccated (dried out).
When the team opens the mummy case the lid tilts back like a hinged lid on a jewelry box as it opens, but the lid is suspended from a sling of lines which come together directly over the center of the lid so the lid should be lifted straight up as it was earlier when Castle opened it to look inside.
Detective Esposito states that the archaeological site was in the lowlands of the Yucatán peninsula. The known kings named Kan Xul reigned in Palenque, well south of that area.
When Castle peeks in the stone coffin at the remains of the Mayan king Kan Xul, Dr. Rachel Walters interrupts him, yelling that the mummy "is over 2000 years old". However, Kan Xul I. (or, as he is more commonly called, K'an Joy Chitam I., i. e. the "earliest" possible Kan Xul) lived from 490 to 565 A.D, so it is considerably younger than that.
Although technically correct, in that the avenue has two official names, no New Yorker refers to 6th Avenue as "Avenue of the Americas" except when reading from a company's letterhead.