When Beckett enters the bank dressed as a paramedic, she is not wearing gloves. When she and Castle move "Sal Martino" onto the gurney, she has a glove on her right hand but her left hand is bare. When she exits the bank and meets Alexis, she is wearing gloves on both hands.
After Trapper John threatens to kill Castle he has a conversation with him. During this conversation the camera changes angles several times. During the camera changes Trapper John's hand placement on his gun changes several times.
Dr. Huxtable was carrying an airsoft MP5K. The winding wheel on the bottom of the magazine is visible in some shots. However, this wheel is only present on airsoft high capacity BB magazines.
It is stated that safe deposit keys do not have numbers on them. That is not always true. Some banks do use stamped keys. (Some others have numbered tags attached by metal rings.)
On the funeral card that revealed the name of the presiding priest, there is a spelling mistake: Priest is spelled "Preist".