During my first go at playing I noticed that when I picked Nirnroot, the sound would stop, but the light/glow remained. After dealing with many (unrelated) technical difficulties, I set these saves aside and started again. Second time, no such thing. Both the sound and the glow are removed when picking the Nirnroot.
So, I'm guessing the bug is that sometimes the glow is not properly removed when picking it? Unless you guys are talking about not being an OCD Nirnroot picker like myself and still having the glow stacking issue.
If I come across a new nirnroot that I've never seen, the glow vanishes when I pick it. If I come across one which I've seen, but haven't seen many times, I pick it but the glow still remains. This is because there's maybe one or two additional rings from the previous times I'd seen it----not enough to create that giant halo, but still more than one, meaning that the plant has been picked and it's current ring is gone, but another older ring remains. I know it sounds confusing but try it yourself if you ever experience a glow that doesn't go away: use the console key (~) and target in the area of the glow. Type
delete. You'll see now that the glow either goes away or gets dimmer. If it gets dimmer you may have one or two more rings, so delete those too. Be careful to save before you do any of this so you don't accidentally delete the entire ground.

But no, it's not that the glow isn't properly removed. Not exactly. It IS being removed, but you probably have other rings from times you passed it and DIDN'T pick the plant. I'm guessing every time we pass a nirnroot plant and don't pick it, a new ring gets added. That is to say, every time we pass it and the respawn timer is reset. So a default ten day respawn period will see this phenomenon happen very slowly. A one day respawn mod (like I was using and have since ceased) will aggravate the problem.