A lot of the answers have focused on how to get involved in coding projects and I think if your goal is to improve your coding projects are a good place to start.

But there's another side to the 'community' aspect of Perl, and it sounded to me like you were looking for ways to be involved in that, not just in projects.

If there's a local Perl Monger's group, you could attend some meetings, and you'll probably find stuff that needs doing that requires enthusiasm, not expert programming skills. For example, at Amsterdam.pm we have projects that involve translation, writing, HTML, organization, etc. None of these will improve your Perl skills, but if you are skilled in one of these areas, your local Perl Mongers can probably put them to use in a way that will benefit the Perl community.

Or, if you want to learn some code in the process and help Perl Monks specifically, you could consider a fairly unknown or undocumented module and try to learn as much about it as possible by reading the code and testing it. When you see something in the code you're unfamiliar with, take time to explore the concept. Then you can write a tutorial or documentation to share the knowledge with other people.