<p>I would probably go for one of these:</p>
<ul>
<li><p><strong>Ask clarifying questions.</strong></p>
<p>These should ideally lead to edits to the answer instead of comment replies.</p>
<p>If the poster made unsupported claims or had a few missing (and impossible) steps in their argument, you can ask them to expand on that.</p>
<p>This could give you a much smaller part to disagree with, in that you don't need to prove the entire counter-claim from scratch, but you can rather just point out the incorrect part of their justification for their claim.</p>
<p>This also has the advantages that they may see the issue in their answer themselves or you may realise you were actually wrong without having to have <em>been</em> wrong.</p>
<p>Of course this doesn't work so well if they don't actually reply.</p>
</li>
<li><p><strong>Ask a new self-answered question addressing the issue.</strong></p>
<p>If the new question would be a stand-alone question that could also be useful to others, then this is indeed probably the best option.</p>
</li>
<li><p><strong>Give a brief summary of why they're wrong and link to elsewhere.</strong></p>
<p>This is actually also what you'd be doing when posting a new question.</p>
<p>If it isn't a common error and you can't find a reference that explains it well, you could always link to <a href="https://chat.stackexchange.com">chat</a> and explain it yourself there.</p>
</li>
</ul>
