Something like this:

<xsl:template match="note//p">
<p class="note_p">
<xsl:if test="generate-id() = generate-id(ancestor::note/ descendant::p[1])">
<xsl:apply-templates select="ancestor::note/label"/>
</xsl:if>
<xsl:apply-templates/>
</p>
</xsl:template>

What this does:

* Collapse the templates together for all p elements inside note, rather than splitting a template out for the first p. This is clearer, allows better code reuse, and is more robust.