Dr. Saroyan refills the dead eye so that a message on the dead man's phone can be accessed with an iris scan. When the phone is used, it clearly requires a retinal scan. These are two different parts of the eye anatomy, and while both are used for identification purposes, the capillaries in either structure would have been too degraded after death to give a positive result.
Having been an FBI agent as long as he has, it's surprising that Booth doesn't realize that excessive cocaine use can cause a hole in the septum.
Dr. Saroyan claims that emerald is easily scratched, and could be chipped by coming in contact with a sharp piece of bone. In reality, bone would be chipped by the emerald (aka beryl), as emerald is much harder.
Angela checks the EXIF time stamp of the images to verify a suspect's alibi, but EXIF data can be easily changed with very little technical expertise. The pictures could have been taken at any time and don't give the suspect any alibi.
As is common among many of the episodes, once the suspect has asked for a lawyer, the interview must be terminated and nothing they say afterwards can be admitted as evidence, even an admission of guilt.
Near the end, Bones tells Aubrey about the "discovery" of the quark. The point of her story is that "when" it was shown to be "true", the detractors were shown to be wrong. However, no scientific theory is ever proven, it can only be disproven, so her story fails to prove the point she believes she is making.