Why shouldn't he have beamed the captain up?
Scotty first says he wants to double-check, then
beams up Kirk! That's callous. If there's a need to double-check, this should be done before the Captain is beamed aboard. If there isn't, Scotty shouldn't waste time doing unnecessary checks.
It always amazed me that a ship the size of the Enterprise only seemed to have the one transporter room. But I don't recall any on-air references to other transporters on the ship
Well, the appearance of the set changed from episode to episode - door color changes, different items decorating the aft wall, sometimes a viewscreen and a food slot near the console and sometimes not. Either the engineers had way too much spare time, or then we are actually witnessing several different rooms.
Also, while the "locally relative" positioning of the room never changed much (because after the pilot, it was a fixed part of the main corridor set), we got conflicting data on the deck where the transporter might be located. In "Dagger of the Mind", not only does the transporter room have a rare circuit board thing on the back wall, but it also delivers Dr van Gelder to somewhere near Deck 14. Possibly a secondary hull location, as the transporter was supposed to be moving only cargo, and the holds are somewhere down there. Indeed, this unique room may be one of the cargo transporters of the ship - possibly with bigger sisters somewhere nearby. Or then there are no bigger transporter, but there are bigger shuttlecraft (as seen in TAS)...