The mistake AND the result = two things. Two things + one verb = plural verb. Belong. Doesn't matter if there are commas or not.
The mistake, or maybe just its egregious result, belongs in the past.
Mistake OR result = one or the other = one thing + one verb = singular verb.
The mistake, its results having turned out so horrible, belongs in the past.
Mistake + verb = singular verb = belongs. Results + different verb = singular verb = having turned out
The mistake, with its horrible results, belongs in the past.
Mistake inclusive of horrible results = one thing = singular verb = belongs. Yes, I know it seems like the 'with' and the 'and' would be interchangeable, but grammatically they're not. Multiple things joined by AND are plural; single things modified by a WITH clause remain singular. Another example:
Ann goes to the movies.
Ann and her brother go to the movies.
Ann, with her brother, goes to the movies. (Not: Ann, with her brother, go to the movies.)
Every day, either Ann or her brother goes to the movies. (Okay, if you put 'go' in there it wouldn't sound *that* horrible.)