My Take
My students love Edmodo and it has grown on me as well. I have used Edmodo as an avenue for teaching Digital Citizenship skills as well as how and what to post in our online discussions. It has a bit of a learning curve, but most of that is due to the many facets Edmodo has: groups, progress (grade book), badges, communities, and tons more features. I think it's important to start with one area and then grow into others.
How I Use It
This is my first year using Edmodo with my 4th graders. Initially, I thought it was best suited for older students, but as I have learned its nuances, I have become a fan. My class uses Edmodo for online discussions and polls as well as posting homework for those who were absent. I also use Edmodo as a portal to other apps and websites for my students. This generally works well since students only need to access Edmodo and the app/website credentials (username/password) is handled by Edmodo. One criticism is that sometimes the apps seem limited and support can fall into the grey area between Edmodo and App creator/owner. Overall, the process is smooth.