Can problems arise when submitting pages with the application/xhtml+xml type?

Yes, they can.

Main issues:

1. Browser support: Not all browsers handle application/xhtml+xml correctly. Historically, Internet Explorer versions before 9 poorly supported this MIME type, treating it as text/html, which could lead to parsing errors. Modern browsers (Chrome, Firefox, Edge, Safari) support it better, but there may still be nuances.
2. Strict parsing: When using application/xhtml+xml, browsers use an XML parser, which is much stricter about syntax errors than an HTML parser. Any minor mistake in the code (incorrectly nested tags, missing closing tags, invalid characters) will cause parsing failure and prevent the page from displaying, showing an error message. In contrast, browsers with text/html often try to correct errors and display the page.
3. JavaScript compatibility: Working with DOM via JavaScript can differ when using an XML parser. Some standard DOM methods and properties may behave differently or be unavailable.
4. File size: XHTML can be slightly more verbose compared to optimized HTML5.

Example of strict XML processing:

<p>
  This is a paragraph.
  <span>This is a span.</p> // Error: the closing </p> tag is before the closing </span>

In HTML, this structure might be rendered, but in XHTML with application/xhtml+xml, it will cause a parsing error.

Due to these issues, text/html is the preferred MIME type for web pages in the overwhelming majority of cases.