Ok. I think that the reason the Volturi didn't mention anything about Charlie because the Bella and the rest of the Cullens never told Charlie that they were vamps and that Bella had been turned into one. Yes, Jacob changed into a werewolf in front of Charlie, so that way he could break the ice and tell Charlie that Bella had changed. In the book, when Jacob was explaining to Bella and the rest of the Cullens what he had said to Charlie, he said that Bella was diff. and that she was more like the Cullens, but he never mentioned telling Charlie straight out that they were vamps. Therefore, he didn't know what they were, he just knew that they were diff. I mean, he may have figured it out on his own, it never mentions in the book anything else about it, but even if he did, he didn't tell them that he did, and the Voturi surely wouldn't know because it was only Charlie that knew, if he even did know. However, since Charlie didn't want to know any details about Bella's "condition", he may not have even looked into it, he may have just left it alone like he told them he wanted to do. Because he didn't want details, anytime he asked them a ques. (like about Nessie), they told him what the public would know. They basically told him enough to where he knew they were diff., so Bella could maintain some kind of relationship with him, and he could see his granddaughter, but not enough to where if the Volturi found out, it would put them in trouble. The only person he knew what they were was Jacob, and that was only because he phased in front of Charlie, and the Volturi don't have any control, nor do they care unless it interferes with them, what werewolves do. The only thing they care about is vamps. At least that's what I remember happening, and it's what I understood as to happening with Charlie and his "I don't want to know any details about it" attitude (like I said I don't believe he checked into it at all on his own time to figure out exactly what they were). Also, know that I think about it, when he would visit, they acted like they were semi-human still, and Nessie would bite him playing around, but Bella would warn Nessie ahead of time not to bite him hard enough to where it would break the skin. And also, on his very 1st visit, the one right after Jacob told him what he was, they had the t.v. going and were watching it, remember Emmett and his "finally (or was it at least) somebody scores around here" comments.
"Look after my heart, I've left it with you."