Just because an answer is accepted does not mean other answers cannot be posted. I agree with you that having an accepted answer makes a question less likely to receive another answer, though. If you believe the accepted answer is incorrect, then other than trying to come up with an alternative answer yourself, you have two options:
Challenge the answerer to provide more justification to the answer.
If it's an active user, it's likely they'll try to dig into it some more. If you can, provide a counter-example to their answer to convince them there's something incorrect. No need to be rude - I've seen many times people delete or revise their answer when politely notified that it might not be correct.
Offer a bounty on the question, and in the bounty description write that it will be given to those that provide a more substantiated answer.
Remember the bounty mechanic is completely separate from the accepted answer mechanic, so you could, for example, offer a bounty on a question with an accepted answer and then award it to an answer which is not the accepted one. The little "this answer received a bounty" mark next to an answer can also help point people to check the answer out, just like the green check-mark does with the accepted answer.
A bounty usually works well on most questions, provided the answer is not too difficult to come up with and that other people are playing the game.
TL;DR - take one (or both) of the emphasized approaches above, but remember to stay polite - people don't just post incorrect things out of malice, they just don't know it's inaccurate.
