Episodes seem to be going backwards in time. The last three episodes have each stated Stardates prior to the previous episode.
Sherlock Holmes never smoked a Meerschaum pipe, only a Brier pipe and only when considering a problem. Sherlock's usual smokes were cigarettes. Also, Holmes said "elementary" only one time in all the books and short stories. The Meerschaum pipe and multiple "elementary(s)" were the product of stage productions and Hollywood. At no time is it stated, or even implied, that Data only researched Sherlock Holmes by the written stories. Data obviously took his characterization from multiple sources.
When Geordi bends over Worf to check his pulse, the rubber outline of the makeup is clearly visible between his left eye and ear.
Data says the energy cloud travels at warp velocity, but when the Enterprise makes its sensor pass, the stars aren't streaking in the background.
When Geordi and Crusher lift Worf to take him to sickbay, Michael Dorn's white undershirt can be seen poking out of his uniform collar.
When Data is impersonating Sherlock Holmes in the briefing room, he notes that ship's sensors show the alien delegates passed through the sensor network "here and here," pointing to the computer screen in front of him for emphasis. When he turns the computer to show Riker and Yar, the screen contains only text, not a schematic of the ship on which he could have pointed out locations.
(at around 13 mins) There is an exterior view of the conference room. The studio framing of the set is visible for a moment as the camera zooms in. (It's still there in the remastered cut.)
The Enterprise is traveling at warp 8 towards the peace conference when it is forced to drop out of warp. After it is seemingly repaired, Picard orders that they resume their heading at warp 6. They are already running behind due to the delay. It makes no sense that they would resume their journey at a slower speed, given the importance of the conference.
When discussing removing Picard from command, the senior officers refer to such an act as mutiny. Removing a compromised officer from command would not meet the definition of mutiny.