1. The sigils are ugly in my opinion (arguments that they help you figure out the type of a variable fall down with references and slices). So I'd avoid arguing against that one if I were you.
2. Perl has warts. The whole $self as first argument thing is one, but there are many others.
3. But, despite the warts, Perl has CPAN. I'm afraid CPAN kills arguments about other languages stone dead. I've tried really hard to move to other languages (C, Java, Ruby) because I don't like Perl's warts, but none of those languages have the simple elegance of CPAN.
4. Speed issues tend to evaporate when put under real tests. Slashdot gets a lot of hits and runs perl. Other sites get a lot of hits and run JSP, others ASP. In the end it all comes down to good design and network architectures.
5. Did I mention perl has CPAN?
6. Java is fundamentally not immune to security problems. That's the most naive thing I've ever heard a developer say. What about cross site scripting bugs? What about SQL injection bugs? No matter what language you're programming in, when you're working on the web you always *always* check your user input. Perl's taint mode makes it hard to avoid doing that, but it still doesn't alleviate security issues.

That's probably not exactly everything you wanted to hear. It's not so much an advocacy argument - the best thing about Perl is CPAN (and sometimes the worst thing about Perl is CPAN, but that's a whole other node).

Update: wedman reminded me of perldoc. That's such an awesome tool I can't rave enough. Show me another language that has as good and as easy to find docs as perl when you're working on the command line.