Perl programmers should first read the man page perlsec(1), which describes a number of issues involved with writing secure programs in Perl. In particular, perlsec(1) describes the ``taint'' mode, which most secure Perl programs should use. Taint mode is automatically enabled if the real and effective user or group IDs differ, or you can use the -T command line flag (use the latter if you're running on behalf of someone else, e.g., a CGI script). Taint mode turns on various checks, such as checking path directories to make sure they aren't writable by others.
The most obvious affect of taint mode, however, is that you may not use data derived from outside your program to affect something else outside your program by accident. In taint mode, all externally-obtained input is marked as ``tainted'', including command line arguments, environment variables, locale information (see perllocale(1)), results of certain system calls (readdir, readlink, the gecos field of getpw* calls), and all file input. Tainted data may not be used directly or indirectly in any command that invokes a sub-shell, nor in any command that modifies files, directories, or processes. There is one important exception: If you pass a list of arguments to either system or exec, the elements of that list are NOT checked for taintedness, so be especially careful with system or exec while in taint mode.
Any data value derived from tainted data becomes tainted also. There is one exception to this; the way to untaint data is to extract a substring of the tainted data. Don't just use ``.*'' blindly as your substring, though, since this would defeat the tainting mechanism's protections. Instead, identify patterns that identify the ``safe'' pattern allowed by your program, and use them to extract ``good'' values. After extracting the value, you may still need to check it (in particular for its length).
The open, glob, and backtick functions call the shell to expand filename wild card characters; this can be used to open security holes. You can try to avoid these functions entirely, or use them in a less-privileged ``sandbox'' as described in perlsec(1). In particular, backticks should be rewritten using the system() call (or even better, changed entirely to something safer).
The perl open() function comes with, frankly, ``way too much magic'' for most secure programs; it interprets text that, if not carefully filtered, can create lots of security problems. Before writing code to open or lock a file, consult the perlopentut(1) man page. In most cases, sysopen() provides a safer (though more convoluted) approach to opening a file. The new Perl 5.6 adds an open() call with 3 parameters to turn off the magic behavior without requiring the convolutions of sysopen().
Perl programs should turn on the warning flag (-w), which warns of potentially dangerous or obsolete statements.
You can also run Perl programs in a restricted environment. For more information see the ``Safe'' module in the standard Perl distribution. I'm uncertain of the amount of auditing that this has undergone, so beware of depending on this for security. You might also investigate the ``Penguin Model for Secure Distributed Internet Scripting'', though at the time of this writing the code and documentation seems to be unavailable.