Continuity mistake: The episode includes Odo as one of the people who is still alive after "200 years." However, in later seasons, it is revealed that Odo was infected with the morphogenetic virus by Section 31 quite a while ago. And given that in those later seasons, he is deteriorating and dying, there is no possible way that the "Future Odo" from this episode could've survived 200 years since he likely wouldn't have survived more than a decade since this episode if they became trapped back in time.
Star Trek: Deep Space Nine (1993)
1 continuity mistake in Children of Time
Revealing mistake: As Kurn is chastising Worf in the infirmary, the actor's prosthetic nose has become detached from the rest of the Klingon make up. You can see the nose wobbling around as he talks.
More quotes from Star Trek: Deep Space Nine
More trivia for Star Trek: Deep Space Nine
Trials and Tribble-ations - S5-E6
Question: Wouldn't Sisko have created a paradox by identifying himself by his real name to James T. Kirk before returning to the future?
Answer: No more so than Sisko posing for a photo in the 21st century while pretending to be Gabriel Bell.
Answer: His last name is something Kirk will forget, since he was on temporary assignment and essentially passing through.
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Chosen answer: No. He's given his name, that's all. Nothing there that might lead to a paradox. If he's gone into detail about his time travelling, that might cause an issue or two, but simply stating his name does nothing.
Tailkinker ★