Exactly - the slight crack (ring crack) around the mid point of the solder joints are cold solder joints and need to be soldered over to reconnect the top of the pin to the bottom of the solder connection. The crack is preventing a good signal.
Right off the bat I can see two cold solder joints in your first picture (on either side of the number 8610 on the pc board).
I dont know what the hot spot is but I would also guess your primary problem are the cold solder joints.
I too had a non fine tip soldering gun (literally looks like a gun w/trigger) and it worked BUT I would not recommend it as it was a pain to be really accurate.
The follwoing site has a good tutorial on how to do a decent solder job. Yours is easier because you just have to "recoat" the joint (without getting any on neighboring pcb board strips - the lighter green strips)
If you do bridge a strip just slightly heat up the offending solder and gently push away with a not too sharp implement.
Essentially you are reheating the joint and addind a small amount of solder to fix.
Cold solder joints on these usually come from hotter components affecting the board over time to the point where the joints become self insulating and dont conduct. They essentially "dry out" and crack.