You posted the .bsp which is the game file, not the .vmf which is the hammer editor file.
I ran through it and the first thing you should work on is brush work and grid work.
Making sure everything lines up, make sure everything is touching
BUT NOT over lapping, ETC.
Its just lighting, your area's are wicked huge and require more lights then you've put in.
he animation on the spawn doors isn't working, one doesn't even let you out
Ya, your trigger brush is a solid, not a trigger multiple, Check out this for how to make a proper door.
How to make a Team Door
Also, im not sure about the cappoints themselves
Check out this.
How to make a CP Gameplay It will help you with setting up the cap points.
To go back to prior though, this is a big one. Before props, CP's, Lighting ETC. Make sure you have your brushwork and grid alignment good.
Welcome to the forums BTW =) !!
Check out the tutorial section and Search tool.