Continuity mistake: Michael invites Spock to play chess. She presents a board with three levels. Later, when the game is underway, the board has seven levels by the addition of four smaller boards. (00:17:50 - 00:21:25)
Through the Valley of Shadows - S2-E12
Continuity mistake: As Gant is trying to inject Burnham's eye, in wider shots the syringe is noticeably further away from her eyeball than it is in close-up shots.
Answer: The planet shown could well be a terraformed moon on the outskirts of the Solar System. The planet is not shown in great detail behind the damaged station.