There is (mostly) no need for linebreaks in perl code, so the answer to your question is as simple as

perl -e '$badxml = `cat /mmf/log/BadXMLXact*`; $badxml =~  /21-digit-n
+umber(.|\n)+/; $& =~ m/\*\*\*.*UID/; $output =  $`; for ($output ) { 
+s/\s{3,}/\n/g; } print $output;'
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Besides that, I wonder about the reason you need to do it as a one liner, when you have a working script? I mean, a one liner is cool but not an end in itself.