I haven't figured out yet how to add a new category, but for dealing with the misclassified items: there's a filter rule that you can set under Settings >> Filter >> "Categorize as: __" which will help to get that sorted out. Too bad the categorization doesn't work backwards for all previously auto-missorted mails!
Reshared post from +Scott Spence
Want the new Gmail and not sure how to get it?
Open up your normal Gmail click on the cog in the top right corner, select configure inbox and boom!
Thanks tofor the video :)