I think it shows up indirectly when there is consistently more discussion about rewards.
I guess we could count the number of posts and comments about MSM. I'd love something more direct though. The line between the dots of something specific being discussed often and the site being less fun and educational is faint for me but I also don't have suggestions that aren't indirect in their own way. Most of the suggestions I'd make would be the indirect measures this post correctly identifies as indirect!
The challenge is interesting though. How can we measure fun? How can we measure learning?
I've discussed measuring learning here before, but I didn't have any great ideas. The best one I had was measuring the deviation of people's zaps from their personal standard in comment threads.