Hello,
I remember one of my electronics lecturers saying (quite rightly) that your first build of any circuit is guaranteed not to work. Don't worry, by the time you are done with this your greatest worry will be how to keep up with a crippling addiction to op. amp's, input capacitors and power supplies. Stick at it!
Just to mirror what others have said, certainly go over your joints again, they look like they didn't have enough flux/the tip was a bit dirty/the tip was a bit cold. Bridges are often there even if you think they aren't - I have found that the flux in your solder can cause some strange issues!
http://www.head-fi.org/forum/thread/64538/is-flux-conductive - this will give you some interesting reading regarding the whole flux issue.
If I were you, I'd re-heat the solder on the joints and while molten, knock the board on it's edge to remove the excess solder, this will let you see things more clearly and potentially resolve a bridge issue.
Then I'd get my iron and using the side of the tip, run it between the tracks. This will further encourage any loose solder to re-collect at one of the pads and break the bridge. It should also tidy it up after you have removed the solder.
After that I'd clean the board with a flux remover (if you have some). If you don't have flux remover I'd get the corner of a fine screwdriver blade and run it between the tracks and pads of the board. This will physically remove anything that shouldn't be there - it's pretty definite. Watch out and don't stab yourself in the palm of your hand holding the board! :)
Also, I see you have used 2 wires to go point-to-point - make sure that the only part of these wires touching the board are the ends that are soldered to the pads. Watch out on the pad next to the soldered pad - where the insulating sheath has shrunk due to soldering, the metal core can touch the adjacent pad. Lift it gently with a fine flat blade screwdriver, careful not to lift the metal pad from the fiber board.
There are many reasons why you'd only be getting amplification on one channel. This has happened to me maybe 30 times and I'm sure that almost all if not all of these times were due to a solder bridge.
I don't understand your alligator clip issue but a picture of your clip setup would be good so we could have a go at answering your issue of an intermittent signal.
Edited by MrTom - 12/5/10 at 3:48am