In "Past Tense: Part 1" Sisko says that the Bell riots are named for Gabriel Bell who died protecting the hostages. Sisko assumed the identity of Bell after Bell was accidentally killed when Sisko and Bashir accidentally changed the timeline. During the riots Sisko is shot but survives. Near the end of "Past Tense: Part 2" one of the guards, Vin (played by Dick Miller) asks how he can help Sisko and Bashir. He agrees to help them escape but takes their ID cards to be placed on two on the people who have died during the shooting. When Sisko and Bashir are back in their timeline and onboard the Defiant Bashir looks-up the riots. In the history records it shows Sisko's picture for Gabriel Bell. Sisko had Bell's ID but Vin took it to place on one of the dead people. History would have shown someone else's picture for Bell instead of Sisko. The IDs did not have photos on them but if they had the picture should have been one of Gabriel Bell.
The hostage-takers repeatedly cock their shotguns. Cocking a shotgun more than once is not only unnecessary, but would in fact eject an unspent cartridge.
Jadzia pushes a manhole open and crawls out of the sewers to infiltrate the sanctuary district. Manhole covers weight about 250 lbs. and typically require tools to move. Trills are not known to have extraordinary strength that would allow her to move it bare-handed. Dr. Bashir later moves the manhole cover back into place with his bare hands as well.
The assault team sent into the processing center uses weapons with red laser targeting sites. When the shooting is over, one member of the team has a red laser dot moving around on his chest indicating that a member of his own team is targeting him.
For some reason, Odo is left in charge of beaming Kira and O'Brien to Earth's past, rather than an experienced engineer or transporter officer. Given that O'Brien himself had to deal with unexpected variables when Sisko and the others were beamed to the past, it wouldn't make sense to have the security officer in charge of the process.
Sisko stated he was worried about snipers picking off himself, Bashir, and the ghosts, hence why they barricaded the windows, yet he and Webb repeatedly meet with Det. Preston out in the open.
In the first part, Sisko makes a big deal of not interfering with history, even allowing a man to be horribly beaten so as not to affect history. Yet they leave two Starfleet communicator badges in 2024 when they return to the 24th century.
B.C. and the others use up-turned benches to block the windows to avoid snipers. The benches are only about 6 feet long. When turned on their side, they leave several feet of windows uncovered near the tops. If snipers were positioned on rooftops across the street, they could still easily see in.
O'Brien narrows the search for Sisko, Bashir, and Dax through time to a period before 2048, as they visited 2048 and found it to be "nothing like the mid-21st century [he] read about in school," saying that "Earth history has been through its rough patches, but never that rough." According to Star Trek lore, World War III engulfed the globe from 2026-2053. 2048 would fall within the most destructive conflict in Earth's history.
When Webb leaves the intake center to meet with Det. Preston, Sisko goes with him, leaving the hostages with B.C. and the other ghosts. According to Sisko, the main contribution of Gabriel Bell (the man he's impersonating) to the situation was ensuring that the hostages were not harmed. Leaving them with an unhinged man like B.C., even with Bashir there as well, runs counter to that goal.