At the end of the episode, Bashir throws two darts at the (off-screen) dartboard (we hear them hit). At the very end of the scene, Bashir throws his third dart; the camera follows it to the board. The first two darts are nowhere to be seen.
When Miles walks over the promenade, he spots Julian throwing darts in Quark's. At that moment he throws two darts. The camera pans and he throws the third, and after Miles talks to him he throws a fourth.
Darts is only played with three darts. When Miles picks the darts from the board, he has only three in his hands.
When Julian and Miles enter Sloan's office (36:16), the room's equipment radically change. A giant computer console disappeared and was replaced with a grey door and the stellar cartography panel vanished. The 0907 panel above miles also was misplaced, and the rack where he found the data pad with the cure is not in the same position it was seconds earlier.
Julian and Miles are inside of Sloan's mind. There are no physical objects involved, nor any reason to assume that anything has to follow the physical laws of the universe. Things appearing and disappearing seemingly at random is perfectly acceptable when in someone's mind.
Julian and Miles are inside of Sloan's mind. There are no physical objects involved, nor any reason to assume that anything has to follow the physical laws of the universe. Things appearing and disappearing seemingly at random is perfectly acceptable when in someone's mind.
Sisko and Dax discover O'Brien and Bashir (and Sloan) when O'Brien fails to keep an appointment to fix Ezri's sonic shower "this morning." Bashir and O'Brien captured Sloan in the middle of the night and set to work trying to extract the information they needed from him. Less that an hour remained until Sloan's death, so it would be strange if it was already morning, specifically later enough in the morning that O'Brien had appointments to keep. And if it was late enough that O'Brien was going to miss appointments, he should have assigned someone to cover for him or he'd know he'd be risking discovery once it was noticed he was missing, as does happen.
Bashir estimates Sloan will be dead in under an hour. He then has to stabilize him, gather equipment, wait for O'Brien to link it up and reroute a number of power relays, then gather more equipment when it is decided O'Brien will go into Sloan's mind along with him. He then states that Sloan will die in 43 minutes. That all would take much longer than 17 minutes to accomplish.
Sloan tells Bashir and O'Brien that the cure for the morphogenic virus that has infected Odo is, "a simple nucleotide marking sequence." If it were that simple, surely a genetically enhanced genius such as Bashir could have figured it out (to say nothing of the entire Dominion effort). Even if Bashir couldn't get the exact sequence from Sloan, narrowing down the field of study that considerably would allow Bashir to figure it out in the time Odo has left without further risking Bashir and O'Brien's lives in Sloan's dying mind.
It was irresponsible for Dr. Bashir not to establish a backup plan for him and Miles to remove themselves from Sloan's mind, such as stationing a nurse to wake them when Sloan showed signs of dying. Further, by not telling anyone their plan, they risked someone waking them up early out of concern, such as when Captain Sisko came upon the setup and didn't know what was going on.
Julian tells Odo that taking the cure is going to be painful. Since it's never been done before, and Odo's physiology is barely understood, there's no way Julian could know that.