Say hi to everyone. This is a pretty old thread, but since it doesn't come up with an answer after 5 pages, perhaps it's worth a bit more talk.
This phenomenon appeared in my new aquarium twice, 1st time after a new driftwood was put into the tank, 2nd time when new water was added into the tank. They seemed to be sticky as various small things were attached to them during their existence. During both times, these things showed up from nowhere and then nearly totally disappeared after a few hours and never appear again.
As such, the possibility of thread algae can be ruled out, as algaes can't show up and disapppear so fast.
They are not cobwebs created by underwater spiders, water mites or other animals for the same reason, and my tank has no such creatures at all.
As I could recall, these things were actually microbes (bacteria, moulds, fungi) in the water. When disturbed by new water introduction or well fed by nutrients brought by things like a new driftwood, they congregate into macroscopic structures similar to cobweb threads.
Hopefully this helps.
Greetings from China.