If I read a partial answer, should I downvote that answer?
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I don't, depends I guess. Personally I'd leave a comment mentioning the wrong part & if the post is edited to correct the mistake I'd add in the +1.
Of course, you have have the liberty to edit out & correct it on your own, if you're so confident.
In general, partial answers are fine if what they already contain is truly helpful. It's absolutely not fair to downvote a contribution that may help the OP at least some of the way. Sometimes, answers are also intentionally incomplete if the OP is asking a "plz send teh codez" or a "fix my wall of code" type question.
Only if the partial answer was given in bad faith (i.e. it is incomplete and doesn't help the OP at all;maybe it was just too lazy to address the hard part) downvoting might be appropriate IMO.