I've been re-reading this passage from the Half Blood Prince, and I'm just not too sure what Dumbledore did to get Mrs Cole to let her guard down around him, and am quite confused as to what Dumbledore did in general.
Apparently Dumbledore thought so too, for Harry now saw him slip his wand out of the pocket of his velvet suit, at the same time picking up a piece of perfectly blank paper from Mrs. Cole's desktop. "Here," said Dumbledore, waving his wand once as he passed her the piece of paper, "I think this will make everything clear." Mrs. Cole's eyes slid out of focus and back again as she gazed intently at the blank paper for a moment.
But what was on the paper, if anything? Alternatively, did Mrs Cole just accept magic happened in front of her but not make a big deal out of it? Or did he discreetly cast a spell on her as her eyes slid in and out of focus?