After Castle's dad is shot, he shows up on his son's doorstep seeking help. While Martha and Rick tend to the wounded person lying on the bed, the wet stains on the pillow change in form and size a few times between shots.
During the autopsy, Lanie says rigor mortis froze the impression of the Iranian Rial into the heel of the victim. Rigor mortis only affects the muscles causing them to tense up, locking the joints in place, so the body is stiff. It has absolutely no effect on any other tissues, especially the skin. The impression of the coin would disappear shortly after the coin was removed due to the residual elasticity of the skin immediately after death.
Calcium ions move into muscle tissues causing them to contract, then ATP breaks it down allowing the muscles to relax. After death the Calcium ions effuse into the muscles causing them to contract, but there is no ATP to cause them to relax. The muscles eventually relax when the Calcium ions slowly leave the muscles which can take anywhere from 8 hours to two days.
Calcium ions move into muscle tissues causing them to contract, then ATP breaks it down allowing the muscles to relax. After death the Calcium ions effuse into the muscles causing them to contract, but there is no ATP to cause them to relax. The muscles eventually relax when the Calcium ions slowly leave the muscles which can take anywhere from 8 hours to two days.
When Ryan returns with the CSU report, he says the techs found high levels of volatile compounds in the sludge on the victim's clothes. Volatile compounds evaporate away completely leaving no trace, so the lab could not have found volatile compounds.
Cashiers' checks are not *totally* untraceable, as is stated. They always have information about the originating bank, if not also the branch of the bank. Visiting that bank may lead to documentation used to issue the check (a letter of authorization, surveillance video, etc.).
The GPS tracker shown at the end has no visible power source and exposed connections. Nobody would design such a device for field use. The device itself would be embedded in some kind of protective material, or something as simple as a coin in the same pocket could short it out.
When Esposito is talking to Beckett, he tells her he is at the "epicenter" of the incident. This word makes no sense in the context he said it, and should only be used by geologists.