Ive done some dam works that didn't work...and now some dam work that is pretty darn good. Your's doesn't look too bad and the amount of work you might have to do it "fix" a lek that can be topped up with a hose might be false economy - ie. cheaper to keep topped up with a garden hose.

From my new experience, clay gravel (which it looks like you have) is pretty darn good and can seal up very well. In my limited experience opinion I'd just top it up and enjoy it unless you have deep pockets..... If I were to try to "fix " it I'd excavate a trench just in front of the water side of the dam and clay face it with an excavator then entire length - but again lots of money and youll still lose water through evaporation.

Oh, and from the way your material is drying out there is a good clay content in it.

Just my 2 cents after about 50K in work over the last few years.