A screen lid can contribute to loss of heat and humidity - but I don't know that arid conditions thereafter can promote mouth rot. Where'd you hear that?

When I was using glass I covered the screen lid just to keep the warmth and humidity in. I left 3 of the 4 corners (bout 2" triangles on a 10gal) open on each corner. Saran wrap wasnt workign very well even when coupled with double sided tape (YES on the outside of lid lol). I found some clear ConTac "paper" which was thicker, repositionable, easier to work with, trim, moisture/mildew free (v "damp towel" technique) and inexpensive. At one point we had no fewer than 8 tanks set up that way.