Problem in soldering a kit
Yes, there are many problems with this board.

Looking at the bottom:


It appears that the solder is not "wetting" the copper traces to any significant degree, probably leaving you with a least a few open connections. You need to apply heat equally to the traces and the leads when soldering.


Looking at the top:


The broken wire on R6 is an obvious problem. That needs to be fixed.
The soldering on the back of the microphone looks particularly bad. Are you sure you haven't shorted it out?
Most importantly, an electret microphone capsule like the one you show requires a DC bias in order to work at all. This amplifier is not designed to provide such a bias. Try it with an ordinary dynamic microphone.