Joshua,
The video helps, but not much, in that you moved it around alot very quickly, and it's hard to focus on a specific area. Intead of panning around on the board, hold the camera still, and zoom in on each section of the board and keep it there for 5 seconds, then zoom back out, move to another section, and repeat the zoom and hold for 5 secs.
Feel free to cut off the legs of the triacs, because 1. it's an electrical hazard since that's where the 12V is switched, and 2, if the legs get bent and touch, you'll get some fireworks!
A few comments - you are putting too much solder on some of your connections, and they have "tails" that could cause problems. It usually shows up as a solder "bridge" between two pins on the IC sockets.
You can get some desoldering "braid" from Radio Shack or another electronics parts store (not Best Buy). When you heat the solder connection and touch the braid to it, it will pull away the solder. Not critical, but something to think about.
If you have a broken pin on one of the sockets or IC's, you need to replace it. Without knowing which pin, it's hard to say if this will cause it not to work. But there's a good chance it will make things act very strangely!
A good voltmeter is very helpful in checking basic things, like if the regulator is putting out the right voltage, and if you have your 12V supply connected corrected, and what voltage is coming out of the output lugs. You don't need to break the bank - you can get a simple one for less than $20 at RadioShack.
