What do you like best?
The software has come a long way over the past 10 years. There is a robust community of administrators and developers is making continual improvements and offering suggestions and support through Moodle's online community. It is free and open-source, and while you should plan to invest some resources in the development, management and hosting of your implementation, our small educational nonprofit saves thousands every year by using Moodle over other commercial solutions. Moodle is also built using web standards that have allowed us to customize a beautiful and simple interface for our students and teachers.
What do you dislike?
The software is *very* resource intensive on a server. Hosting it became a very expensive proposition, but now we host it with a company only provides Moodle hosting and has several scalable plans that can grow with our organization. Also, the back-end can be a bit difficult to navigate & find what we need at times: it sometimes feels clunky & counter-intuitive.
Recommendations to others considering the product
Unless you have your own server and a dedicated professional who can manage it, I strongly recommend researching a vendor whose business is to serve Moodle; consider a cloud implementation. The software is very resource intensive, depending on the number of concurrent users, and a managed-hosted solution has made a huge difference.
What business problems are you solving with the product? What benefits have you realized?
We use Moodle to securely host private course content to students who are matriculated as well as others who sign up for a short course here and there. It allows us to track student progress, their usage of learning resources, collect and grade homework, and securely host files with smart integrations with Google Drive and Dropbox.