It does have so many good elements in it... and Joan Collins shines as Edith Keeler.
However, it is quite a stretch that McCoy would be able to escape from the Enterprise in such a delirious state. To have the clarity of mind to operate the transporter... given his character, you'd think he wouldn't even know how to operate it.
I'd see it more plausible like this: McCoy is running around the decks, knocks over someone with a phaser, and takes the phaser weapon. He then storms into the transporter room and forces the technician to beam him down. One could argue that the transporter tech could just load him into the pattern buffer and hold him there until security arrives, then rematerialize him on the platform and stun him. But you could have a young technician who panics and just does what the doctor demands of him--beaming down to the surface.
Of course, then there's the peculiarity of where people get geographically positioned when they travel to a particular time. Why that particular spot and not somewhere else? I do like how Kirk and Spock appear just before McCoy does, to prepare for him. The leeway of a few days makes sense due to the lack of precision with physically leaping into the portal.
Otherwise, I think most of the other elements work rather well.
