Can there be problems when sending pages with content-type application/xhtml+xml?

Yes, they can. The main issues are related to backward compatibility and browser handling peculiarities:

1. Incompatibility with Internet Explorer (and older browsers): IE versions before 9 did not support application/xhtml+xml and treated such pages as text/html, which could lead to incorrect rendering due to different parsing rules.
2. More strict parsing: XHTML requires a more strict structure and syntax (all tags must be closed, tag and attribute names in lowercase, etc.). Even a small syntax error can cause the browser (if it processes the document as application/xhtml+xml) to show a parsing error instead of trying to fix it, as happens with text/html.
3. JavaScript limitations: DOM API in the case of application/xhtml+xml works with XML DOM, which differs from HTML DOM. Some standard HTML DOM methods and properties may be unavailable or behave differently.
4. Impact on SEO: Some search engines may have difficulty indexing pages with such content-type, although this issue is less relevant now compared to earlier years.

Overall, text/html is a more reliable and compatible option for most web pages. Using application/xhtml+xml makes sense only in very specific cases requiring XML strictness, such as when integrating with other XML technologies or generating SVG within a document.