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.
Trials and Tribble-ations - S5-E6
Continuity mistake: On the old Enterprise bridge, Sisko is shown at a bridge station, and the person next to him, close to Dax's position, is wearing a gold shirt. When Kirk comes onto the bridge, the person next to Dax now has a red shirt, which was the original crewman's shirt in TOS.
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 ★