Based on input and my $.02 of book smarts, here are my next thoughts. The slope of the upstream side of the dam should be no less that 3:1. The slope on the downstream side should be no less than 2:1 with good clayey soil or 3:1 where additional silt is in the clay. The pics of downstream do, indeed, appear to be steeper than 2:1. If the upstream side is similar, faux pah #1.
In a good clay subsoil at the dam, a core may not be needed, but a mechanical bond between the foundation and the dam above should be prepared. This can be done by scarifying or disking to provide a bond with the material in the dam.
What is the height of the dam compared to the top width? Here are your targets: Ht 10' = 6' min top wth, Ht 11-14' = 8' min top wth, Ht 15-19' = 10' min top wth, Ht 20-24' = 12' min top wth. All this above dimensional info spec's the ideal min mass.
Now, on to the compaction. Was there sufficient moisture in the clay soil? Could you grab a half fistful, compress it into a firm ball, and shake it violently while loose within your fingers and it doesn't disintegrate nor does water droplets fly off? Mike Otto, PB excavator extraordinaire, says to put the hand-compacted ball into a bucket of water; if it falls apart quickly, no good...if it hold together, good.
Lastly, you guessed the blade width of the dozer at 6'. This is where I ask my mentors to assist. At 6' wide, this is a small dozer...right? Tn Hillbilly would pat me on the back for this; dozers exert very little pressure for compaction. This, combined with a small unit, provides nil. You may very likely be lacking considerably here.
Wow, your timing is really something...you still have the bux in YOUR bank. M. Nature has, in her strange and unexplainable manner, smiled on you with a failure. A level-headed business discussion with your contractor is in order. Your offer to bring in the sheepsfoot at your cost is equitable and shows your intent on fairness. IMO, if the reaction is negative, time to look for help elsewhere and prepare for a lien/legal action. I hate this last sentence; I suspect you will find a fair ending...give it a fair chance. (you may want to protect BOTH parties by putting the expected results in writing).
This thread may help: dam protocol This is my call to PB assistance for a similar situation. You will also note an interesting opposing view by h2Ofwlkillr regarding successful compaction by use of only a dozer.