Hey Ryan,
In my younger years, I did a lot of construction work, built decks, fences, clubed basements... it looks to me that you have done a very nice job on the joints. I wouldn't beat yourself up over those joints-they look very good. Unles you have an electric compound mitre saw, you will almost always have some small gaps here and there.
To fix the gaps, and have your stain cover better, try running a thin bead of thinned elmers glue down the gap, then pack some sawdust into the gaps. Finsh with a light sanding.
You may also want to check with you local hardware store, I think someone makes a glue that takes stain.
Hope this helps,
Brian.