First off, make sure that you're not confusing answers and comments. Answers can be edited indefinitely, by anyone, at any time. Comments can only be edited by the original poster within the first 5 minutes of submission (and ♦ moderators).
So yes, an answer could change drastically, even multiple times, since you first looked at it and voted. That's why we allow votes to be changed after an answer is edited. If you revisit the answer (or look in your vote history in your profile), you can change your vote as appropriate (or simply retract it).
But comments can really only change within the first 5 minutes. So yeah, assuming that you vote on a comment immediately after it is posted, and the person makes a drastic edit to the comment within the first 5 minutes, you could have voted for something that you no longer agree with (there is no downvoting for comments).
Then again, this is extremely rare. Someone would have to be intentionally trying to dupe people, and you would have to be vulnerable. All you have to do to prevent this is to be less zealous with that mouse. There's no time limit on casting a comment vote; you don't have to hurry.
Also, comments that have been edited are specially indicated as such: that's what the little pencil icon is at the end of it. If you hover over the pencil with your pointer, you'll see a tooltip that says how many times the comment was edited.
Finally, keep in mind that all votes are anonymous: even if this did happen, no one would be able to connect your vote (and implicit support) back to you.
So I don't really see this becoming a problem. If you see someone abusing comment edits like this, you can flag one of the comments for moderator attention and ask them to look into it and/or ask the user to stop doing this. Edits are supposed to be for fixing typos, or maybe adding some more information. If you want to change your position entirely, just delete the original comment and start all over. The poster of a comment can delete it at any time, regardless of how many votes it has.
If it was decided that something should be done about this, I would suggest extending the period when users can cancel their upvotes on comments to 5 minutes, which would make it coincide with the 5 minute window in which the poster can edit. That way, if a comment you voted for was edited to say something you no longer agreed with, you could still remove your vote. But I don't think this is necessary.