First of all, pride is the pinnacle and the cause of every other sin. So a complete character would have a self-centered streak as an automatic checked box and you can choose a myriad of other weaknesses to supplement and be fed by the said pride, i.e. self centeredness.

Another thing you absolutely must have is a weakness for what they want, the sort of 'I want' tilt that everybody has, deep where nobody can see. That and emotions often seem to be stronger and tries overrule reason, which also goes for anybody.

Those are basic rules that are 'automatic checkboxes' if this were a 'choose some flaws below' type of thing. Anything else is non essential and particular to the character.

I dunno, my favorite villain type is the one who's seductive, charming, attractive, and unnervingly knows your weaknesses, and every move you take he can corner you. Somebody like Annatar from the Silmarillion.