If you are interested in something 'useful', instead of just solving book-problems, try browsing CPAN and looking for modules in need of sub-classes. There are quite a few modules that are made to work with various logs/wikis/programs, etc, that could always use more plugins for translating to whatever you happen to be conversant in. Putting together a plugin, as well as a test suite and module packaging for one, will show you around more than just the language, but also the culture and tools of Perl. Most of the time the authors of the base classes have put some thought into making subclasses easy and clean to make.
And, if you get stuck, the author of the original base will probably be willing to help you (especially if you show you are trying!). They'd probably be flattered. (I know I would. ;) ) Even if you don't want to set up a CPAN id, they'd probably upload it for you if you can provide something that works.
Projects off the top of my head that could use such include Pod::Simple::Wiki and <shameless_plug>Mail::Log::Parse</shameless_plug>. I'm sure there are others.
And in the end you'll have the satisfaction of having written something people actually use!