I apologize for the length of the following post.
I like the map. It looks like, if done well, it could be a very nice map. I'm not a big mapper like a lot of these guys, but I've got some comments/suggestions.
Like what one said before me, the BLU spawn's front door is in the open from across the map. Do what he said, where you should add rocks or a hut or something.
Since your map is mainly a one way route to Point C, you should add a forward spawn after BLU caps Point B. I say put it right where Blue Door 1 and 2 are, as that's not too far up, but not too far back.
I find a similar issue between A and B. Since you're moving from a rocky alpine environment to a lumber mill alpine environment, maybe make that clear by adding some lumber to help make that area less open, and make your map look better.
Addressing the concern of RED's spawn doors being too close to the points, and Door 2 being open for point B, letting RED come in from behind: I suggest removing Door 1. Door 2 could lock once A is capped, Door 3 could lock once B is capped. Also, either remove the staircase that is right outside Door 3 leading to B, or move B's door a little farther away (I like the former).
Addressing the concern of Point C being hard to cap: Like I said before, I'm not an experienced mapper, so those out there like Youme or Nineaxis who know more than me could correct me on this, but I say you move Point C to the top left corner. Not in the building, but right below it. It looks like you have a wall or something there, blocking it's direct sight from Point B, which could make it a nice place to put. Also, make the raised platform on the far left have a wall so that BLU cannot be right on top of the point (We want to make it easier for BLU to cap, but not too easy).
I supplied a (poorly done) picture of everything I said as I'm not good at describing. I edited your sketch by using the erase tool, line tool, and Selection tool in Paint and uploaded it to Imageshack.