Does 「わるいところ」 also have the meaning of "negative aspect"? This I heard from a Japanese friend. If not, how would one say "the negative aspect of X"?
Yes, わるいところ could indeed mean "negative aspect." ところ literally means "place", and this can be broadly interpreted as an actual place, a point in time, a characteristic, etc.
Some other examples of ところ used in the broader sense:
I like the simplicity of the dress. (Characteristic)
He has no pride. (Characteristic)
The train just left. (Point in time)