When he was aboard the Starship Reliant, did Pavel Chekov state his position as being First Officer or was it Science Officer?
Do you think he would have been a good Captain, say of the Enterprise-B?
He indeed says, ``Log entry by First Officer Pavel Chekov'', which is abnormally clear-cut and difficult to dispute for this sort of thing. I don't think there's anything given to suggest whether he's also Science Officer, although since we haven't really had that sort of doubling outside of Spock I'd bet against it.
I don't think we have any real basis to go on about whether he'd be a good Captain. Really, he never had the chance to show command skills in the Original Series -- you have to get Kirk, Spock, Scott, Sulu, and possibly a semi-regular like DeSalle out of the way before he can be left in charge of the bridge, and similarly any landing party you have Kirk and Spock there taking all the interesting decisions. (Chekov was given the bridge one time, in ``Journey to Babel'', but Kirk was at that moment grasping for anyone not vehemently unqualified and Chekov was probably just the first in the line of sight.)
He seems to have performed his various navigation and science officer duties well, and he seems to have been satisfactory as first officer. But really the only time we get to see Chekov taking command is in Generations, when he whips up a medical staff out of the people right around him, and even there his adventure is very subordinate to Kirk's.
Chekov seems to have done well enough there, though; apparently all the people beamed over from the Lakul survived (the dialogue is not as air-tight as I'd like about this), which considering the lack of medical staff indicates he must have organized the first aid quite well. That's a good mark in his favor.