About that money. With the size of those bills my wife and I questioned the size of men's wallets back then!

Yes, it was the hat.

I seem to remember the apartment was in a block originally bought by Dimitrios. Mr Peters' elation at receiving the money was sadly short lived. He looked down and I think he saw the hat and scarf Dimitrios had been wearing earlier laid neatly on the table. He knew Dimitrios had outsmarted him again and would not show him any mercy.

If this had been a story in recent times perhaps there would have been a tracking device buried in the money (this ploy is often used in ransom situations). Could this scene somehow explain how Demetrius found them so easily?(this was never explained)

Just saw the film and remember noticing that scene, but I couldn't figure out what he was looking at either. It was a pile of money and my reaction was that he realized maybe it wasn't all real cash but that wasn't the case. In retrospect maybe he suddenly realized that Demetrios was standing behind him? It was right after that we see him. Only explanation that fits I think.