Here's how I'd do it, using the Muenchean method. Google 'xslt muenchean' for more info from smarter people. There might be a clever way, but I'll leave that to others.
One note, I avoid using capitals at the start of xml element names, eg 'File', but that's up to you.
<?xml version="1.0"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
<xsl:output method="html"/>
<xsl:key name="files" match="/Problems/Problem/File" use="./text()"/>
<xsl:template match="/">
<html>
<body>
<xsl:apply-templates select="Problems"/>
</body>
</html>
</xsl:template>
<xsl:template match="Problems">
<xsl:for-each select="Problem/File[generate-id(.) = generate-id(key('files', .))]">
<xsl:sort select="."/>
<h1>
<xsl:value-of select="."/>
</h1>
<xsl:apply-templates select="../../Problem[File=current()/text()]"/>
</xsl:for-each>
</xsl:template>
<xsl:template match="Problem">
<p>
<xsl:value-of select="Description/text()"/>
</p>
</xsl:template>
</xsl:stylesheet>
The idea is, key each File element using it's text value. Then only display the file values if they are the same element as the keyed one. To check if they're the same, use generate-id. There is a similar approach where you compare the first element that matches. I can't tell you which is more efficient.
I've tested the code here using Marrowsoft Xselerator, my favorite xslt tool, although no longer available, afaik. The result I got is:
<html>
<body>
<h1>file1</h1>
<p>desc1</p>
<p>desc2</p>
<h1>file2</h1>
<p>desc1</p>
</body>
</html>
This is using msxml4.
I have sorted the output by File. I'm not sure if you wanted that.
I hope this helps.