The Visitor - S4-E3
Corrected entry: Even though this episode's future is an alternate future, the ranks of both Bashir and Jadzia are incorrect according to the time. They both have the rank of Commander which is inconsistent to their age and to Nog's promotion to Captain. They should have the rank of Admiral or even retired from Starfleet.
The Way of the Warrior (2) - S4-E2
Corrected entry: For strong warriors, The Klingons soon fall over after a few punches from Major Kira.
Correction: Major Kira is an excellent hand-to-hand fighter. She could easily have hit the Klingons hard enough to knock them down after a few punches, especially if they were not expecting her to put up such resistance.
Corrected entry: In the room where the Ferengi wake up after they crash on Earth an oscillating fan is visible on a cabinet. It looks like one I could buy today instead of the style in the 40's. The cage is far too enclosed. (00:16:25 - 00:23:50)
Correction: While the less enclosed fans were popular in the 40's, more enclosed fans did still exist. In fact, some fans from the 40's look like fans you could buy today.
Correction: There is no reason to assume that they would be admirals at any specific point of time. People are not promoted simply because they have gotten older. It is a combination of personal merit and the current needs of Starfleet. And so far as retirement, life expectancy is different in the future so there is no reason to believe that they would have retired at any specific age unless we are told a specific age at which starfleet officers retire in that century.
Garlonuss ★
Also as Bashir and Dax were both blue-uniformed science/medical officers, their career paths would not have taken them to command of a starship (although Dax, as well as Crusher and Troi could stand in for a while). Unless they got a transfer to the command division (as Crusher had in "All Good Things") they wouldn't get to be captains and commander would be the highest they could go.
Also, given that they are still in the blue science/medical division uniforms, the rank of Commander is probably the highest they can go without transferring away from their preferred fields and into the Command division (and we all saw how well that worked for Crusher in "All Good Things...").