The pics help.

The only rock I see in your dam trench is near the pond side water level. If that is correct, that is fine. MANY ponds have rock placed on the dam facing the pond after the dam is constructed.

I do not see any significant rock issues in your dam core. (Unless you are seeing rock in person?)

Even your core fill looks fine to me.

Most organic material in the soil or in the muck at the bottom of a pond is black. (Usually because it is isolated from oxygen and aerobic bacteria.) However, not all black material is organic muck!

I have black subsoil material on my farm. It is almost 100% clay. It packs very well, and has such a low organic content that it will not degrade over time.

Can you grab some of that black material in Pic #3? Wet it a little and try to make a small snowball. If you can pack it, that is good clay. Generally, if you grab black "muck" organic material from the bottom of an old pond it will not pack.

Can you go to a safe part of your trench and deftly make some cuts with a shovel into the side walls? (Trench safety first!) If you see large rough layers, that is constructed by the pond builder. For example, if they built up the core in 6" lifts, you might see that a little as they pushed in some slightly different colored material each time.

However, when you start to see very fine layering in your shovel cuts, that means you are into naturally deposited material. You are then below the core trench excavation and back fill.

More wild speculation from a guy not on the site:

I do not see a "rock problem" as I described in my previous long comment. (It might be there, and I am not seeing it in the pictures. You are the eyeballs on the ground.) It does sound like you do have some minor leakage through the dam. That may be due to an imperfectly constructed core trench. It may even be due to a properly constructed core trench! Even expert pond builders do not give leak guarantees. The soil materials they work with are too variable, such that pro builders sometimes have to go back in and find and repair leaks.

(Was your neighbor the pond builder? If he says he put in a core trench, that still sounds likely true at this point. However, if your site is "clay poor", then perhaps there was a little bit of forced skimping on either the height or the width of the core trench?)

Dam leaks are notoriously difficult to find. I believe they are usually found by very delicate excavating on the back side of the dam while the pond is full. (I am a geologist, NOT a dam construction expert.)

Perhaps search the archives and read some of the "dam leaking" threads. Some of those contain excellent histories about finding a leak and then repairing the leak.