You want to use the block form of eval. Here's the quick and dirty:

next if ( ! eval { $rss->parse($url2parse); 1 } );
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A slightly more involved example:

use English qw( -no_match_vars );

eval {
    $rss->parse($url2parse);
};
if ( $EVAL_ERROR ) {
    my $err = $EVAL_ERROR;
    if ( $err =~ /bad feed or whatever/ ) {
        next;
    }
    else {
        # some error you weren't expecting
        die $err; # rethrow it
    }
}
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If you don't use English, $EVAL_ERROR is known as $@. See perlvar.