When Alex/Dr. Blake questions Dr. Smith in prison, she calls him "Mr. Smith", to which Dr. Smith objects (rightly so). When she leaves he stops her by saying, "Agent..." and she responds by saying, "It's 'Doctor' [Blake]. Unlike you I still have my degree." Except you cannot lose your degree, and Dr. Smith should still be addressed as "Doctor". When a doctor goes to prison for crimes that violate the Hippocratic Oath (e.g. murder, manslaughter, rape, et al) their medical license is usually revoked, meaning they cannot legally practice medicine anymore. However, they still graduated medical school and earned the right to be called "Doctor", even if they cannot work as one.
The goof item below may give away important plot points.
When Tony wakes up in the hotel room and realizes his leg has been removed, it is quite obvious that his leg is actually hanging down through a hole cut in the mattress evidenced by the sheet's up and down movement whenever his "stump" moves.