The Galileo Seven (no relation to Blake's)

[J.T.B.]

Was then Chekov the first ensign we saw on screen so they made a mistake when they put him in a crewman uniform and it went on from there.

No, as @BK613 pointed out, the first ensign onscreen was the personnel officer in "Court Martial."

Was Chapel an officer?

Nurses in the armed forces have generally been officers in the 20th and 21st centuries. Chapel was also said to have a background in biomedical research, so very likely she had officer-level educational qualifications. Her actual rank is never specified, but ensign seems to fit the evidence best. In STTMP she was a lieutenant, the same as Chekov.

 

[Timo]

FWIW, Chapel's rank is specified as Lieutenant in TAS "Mudd's Passion", where she also sports the appropriate braid. Further support for Ensign in TOS, so as not to make the jump too big?

Apparently the promotion is not due to her finishing her doctorate, since she never gets addressed with that title in TAS. Odd that she is still a mere Lieutenant as TMP unfolds and her doctorate gets a mention, though. Did she choose to remain a nurse with MD credentials through TAS for some reason, and the promotion did come for that reason after all? I mean, we don't see full Lieutenants as nurses anywhere else. (But Ogawa gets the junior grade without ceasing to be a nurse.)

Timo Saloniemi