Easily fixed by excluding whitespace:

#! perl
use strict;
use warnings;

for ('Look here: http://example1.com/cool.mp3 for a great listen!',
     'http://example.com/ this is some text about my .mp3 files.')
{
    print "Match: $1\n" if m!\b(http://\S*?\.mp3)\b!;
}
[download]

Output:

18:26 >perl 1664_SoPW.pl
Match: http://example1.com/cool.mp3

18:26 >
[download]

Hope that helps,