Yes Perl is vulnerable as almost every computer language.
(Race condition,NULL poison...)
But Perl has some feature that you could use to greatly reduce the risks :

• Suidperl
• The Taint mode
• The automatic memory allocation
• Modified (s)printf (no format string attack..)
• Tons of open sourced robust security tools/modules : For encrypting, signing, communicating...

Perl provides you many tools to produce safe code, but also enough freedom to screw your security...

Anyway, to my mind, the security shouldn't be enforced by the language but by the programmer.
You should better watch carefully your code logic to ensure security
(this combined with a decent OS (which excludes windows ;-) should provide enough security)

UPDATE :
Don't hesitate to use Super Search with 'security' as keyword to find tons of interesting threads...
Perlsec and the Camel's chapter about security should be mandatory too...

"Only Bad Coders Code Badly In Perl" (OBC2BIP)