<p>Ignoring the IE case, are there any other browsers that can't understand the application/xhtml+xml content type? And what about the search engine spiders?</p>

<p>I could not find any answers on the web that would not be a few years old and thus possibly inaccurate.</p>

<p><strong>Edit:</strong>
Somehow related question: <a href="https://stackoverflow.com/questions/278746/what-problem-does-xhtml-strict-solve">What problem does XHTML strict solve?</a></p>

If you ignore 80% of the market (yes, IE) then XHTML is very well supported, and search engines have no problem with it whatsoever (after all, XHTML is a lot simpler to process).
Overall, XHTML support isn't really a problem. IE doesn't support it, but as long as it's served as a contenttype it does understand, will render it okay anyway, and everyone else support it properly.
Do you have more specific use cases in mind?