system only returns when the command that is launched returns. In your case, the first system only returns when mozilla is finished, so the script only continues after mozilla has exited. One way to deal with this is to fork off a child to run mozilla. Something like:

#!/usr/local/bin/perl -w
use strict;
die "Something fishy: could not fork.\n" unless (defined(my $pid=fork(
+)));
if ($pid) {
  # $pid has a non zero value, so this is the parent
  sleep 5; # give mozilla some time to start up
  system ("mozilla -remote openURL (www.perlmonks.org, new-tab)");
  system ("mozilla -remote openURL (www.metafilter.org, new-tab)");
  system ("mozilla -remote openURL (www.slashdot.org, new-tab)");
  waitpid($pid,0); # wait until mozilla is finished
}
else {
  # $pid is zero, so this is the child
  system ("mozilla");
}
[download]

This code is untested.

If Windows supports backgrounding a process from the shell, another solution is to run mozilla in the background in your first system(), but I have no idea whether that's possible or not.

CU
Robartes-