It really seems like Sheriff Mills is beginning to be a hunter in her own right. She dispatched that vampire all on her own. I don't even know how she knew it was a vampire, but she knew how to kill it. Sometime next season, the boys are probably going to be calling her for help with a case, instead of the other way around.
That scene with the struggle between Dean and the vampire was definitely supposed to touch on the Mark of Cain. Dean is starting to become too aggressive and violent. I mean, he's always been rather violent (he's a hunter, after all), but the Mark is starting to make him really enjoy it. The Mark is making Dean more demonic, and it's entirely possible his eyes may turn black in a few episodes.
I'm not sure they ever answered the question about the girl's name. I know the reason why the momma vampire called her by a different name was because she was naming her after her own daughter. However, the girl was referred to by three or four different names during the course of the episode. They never explained why the other vampires called her by different names. I mean, they could just be doing the same thing, but what are the chances of them all losing relatives whose names are variations of Ann or Alex?
