Personally, I would have nightmares knowing to have such a this program out in the wild...

Some suggestions if you cannot resign this task...

• use strict; use warnings;
• use taint-mode (-T flag)
• when calling external programs, use absolute paths
• check return status of external programs
• convert this concept into a module or at least a sub with proper arguments and defined exit state
• never ever operate on /etc/shadow directly. Create a new temp. version (perm: 0600). Make a backup of the former /etc/shadow. Rename new temp. version to /etc/shadow iff no error has occurred until this point in execution. Better: Use your OS tools to manipulate /etc/shadow instead of manipulating it directly.
• check input (e.g. $benutzername = ".*" probably has an unpleasant effect...)
• define ENVironment (e.g., PATH; LD_LIBRARY_PATH, etc.)
• sudo might be useful
• have a look at Security in CGI Programming and perlsec...
• restrict pwd changes to certain users (good, you already planned that)
• think about some load-limitation other other restriction that helps to reduce the rate an external attacker can crack accounts... (sleep 5 is cheap)
• log every change (time, user, IP, etc.)
• allow good passwords only (spawn a password-checker)
• restrict access to certain IPs (e.g. intranet) only
• see also: Passwd::Unix, Passwd::Unix::Alt, Expect, Expect-FAQ, How do I send a password to a command I start with Perl's Expect.pm, Changing passwords using Expect.pm through ssh on a large number (75) of systems
• ...

Good luck.