My approach would be:

1. find all <a ... </a matches and extract them
2. search them for <a strings

like this:

#!/usr/bin/perl -w
use strict;

$/=undef;
$_ = <>;

my @ina = /<a(.*?)<\/a/isg;
print "Found unterminated <A> tag containing: '$_'" for grep { /<a/ } 
+@ina;
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This is not a perfect solution: it does not take into account things like:

<a href="ok" name="<a> go on">this is ok</a>
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but since you're dealing with imperfect input, it should be enough to give you a hint. :-)