Corrected entry: During the previous episode, we find out that Dr. Bashir has been replaced by a changeling. But for the changeling's ruse to work, he would need to carry out all Bashir's duties. Which means he'd need all his medical knowledge. Bashir graduated second in his class at Starfleet Medical Academy. To learn all that Bashir knew would have taken longer than the Dominion and Federation knew about each other. Not only that, but to pull off all this changeling pulled off, he'd need intimate knowledge of Starfleet, Bajoran and Cardassian technologies. There's no way a changeling could have learned all that knowledge in the time alotted. Even if you use the excuse of the Great Link, the Founders would still need the time to amass the knowledge and at least one of them to learn all the medical techniques Bashir would have known to transfer that knowledge to the others, otherwise it would have been a dead giveaway Bashir wasn't really Bashir.
Corrected entry: Odo would have already been infected by the virus by this point. He passes the infection to The Great Link in episode 4-26. It's highly unlikely they would have found a cure on this planet with little medical supplies and the elder Odo never mentions it. Odo should not have survived to see the crew of the Defiant return.
Correction: At the end of Episode 4-26 Odo is turned, according to Doctor Bashir, into human and does not have any contact with an Changeling from the Great Link until the Dominion captures DS9 at the end of Season 5. Since no one was ever worried that the Changeling Virus was any danger to humanoids it's quite probable that Odo was "healed" by his people's punishment and did not carry the Virus during any Episode in Season 5, including this one.
Correction: The virus is accelerated by shape-shifting. The Founders were affected quicker than Odo, even though he was infected first, because they change their form more often. If Odo did not change much during the 200 years, he would have remained unaffected.
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: The changelings are highly intelligent and this one was specifically selected to replace Bashir, so undoubtedly it underwent extensive training in preparation for this mission.