Here you go:

$ cat TonyNY.pl
#!/usr/bin/env perl 
use strict;
use warnings;

my $userid   = 'u';
my $password = 'p';
my $server   = 's';
my $actionid = 'a';
my $pkgname  = 'p';
my $wgetlog  =
    '/usr/sfw/bin/wget  -r -np --reject "index.html*" --https-only --n
+o-check-certificate --user ' . 
    $userid .  ' --password ' . $password . ' https://' .
    $server . '/dev/' . $userid . '/' . $actionid . "_" . $pkgname . '
+/';

print "$wgetlog\n";
$ ./TonyNY.pl 
/usr/sfw/bin/wget  -r -np --reject "index.html*" --https-only --no-che
+ck-certificate --user u --password p https://s/dev/u/a_p/
$ ./TonyNY.pl | wc -l
1
[download]

Take this SSCCE, and put your own variable content in it. You'll soon find where you are going wrong (Hint: It's your $actionid value which is problematic)

And just to solve the XY problem as well, see LWP::UserAgent or any of the other web-retrieval tools on CPAN so you don't have to shell out in such a convoluted fashion in the first place.