Plot hole: Apparently when it came to taking the ship into the asteroid, the entire bridge crew conveniently forgot that Galaxy class federation starships can separate. The obviously prudent course of action would be to separate the ship and send the star drive section (the narrower section) into the asteroid while the saucer section (the wider section) stood guard outside. The only reason this wasn't done was to provide drama for the rest of the episode when the Romulans collapsed the entrance to the chasm.
Continuity mistake: In the opening log entry of the first episode, Picard says that "I have been informed that a highly experienced man, one Commander William Riker..." He sounds as though he has been assigned a First Officer without knowing him. However, in this episode he tells Pressman that he read Riker's file, and wanted him, based on Riker's adamant refusal to obey an order that went against his safety protocol.
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