|Problems? Is your data what you think it is?|
First, there is a lot of activity about booking.com lately, who do all their backend work in Perl, and are actually looking for Perl developers. I personally know the team that is contracted to actively help booking.com's initial screening. If you or someone you know are seriously interested in a *hardcore* Perl gig in Amsterdam, PM me with your contact mail (sawbonessurio AT gmail), and I'll put you in touch with them.
AFAIK, a lot of film websites and film revenue databases are written on perl.
Coverity, puppetlabs, Big Blue Marble, onyx neon, etc... etc...
Big chunks of weborama (Europe's largest online marketing firm) use perl. AFAIK, they are rewriting their entire system to Perl(!) because it outshines their other setups!
This is not big, but here's a newest addition to Perl based web applications: http://www.steve.org.uk/Software/slaughter/guide
Slaughter is a tool which is used to automate the configuration, maintenance, and management of a large number of servers. Slaughter is implemented in perl, a language which has traditionally been suited to system-administration tasks, and thanks to CPAN there exists a wide range of utilities and libraries which are available to you. Although Slaughter is a modern tool, written from scratch, it was significantly inspired by CFEngine. (The supplied primitives are very similar, but the client-server model was replaced by the more flexible system of transports.)
Thing is, as you rightly mentioned yourself, there's some unwanted negative publicity about Perl being some kind of washed up, primitive language, so companies don't go around advertising that they actively use Perl.Seriously man. Just go with what you know best.
P.S: I have some free time on my hands. If you need some extra pair of hands on deck to help you with this FOSS application, don't hesitate to reach out to me (sawbonessurio AT gmail). :-) Glad to help you with the coding. :-)
Have a nice weekend!