Personally I wouldn't house snapping turtles with a red ear slider. Especially since snapping turtles can be aggressive, and they outnumber the slider 3-1. Mixing turtle species like above usually only works out best in large tanks, and from the looks of the tank in the picture it isn't very large. If they are all fighting over the same basking spot, or even food for that matter, you may have a problem.
I keep common snappers with other species and have never had a problem, most people think that snappers are aggressive all the time, but they only get nasty when they are taken out of the water, and even then not towards other turtles,When on land I have seen my snappers get walked on by sliders and they pay no attention to them at all, But it does look as though your snappers are missing the tips of their tails.
Common Snappers are the worst tail nippers I have ever encountered in my life, especially as young. I am not surprised to see the shape those tails are in, given the amount of serpentina being kept together.
I would be more worried, especially for the time being, of those tails being bitten more and more and serious risk of infection or further irreversible damage to sensitive tissue. That problem won't fix itself.
The serpentina will not be able to hide from each other as easily as the Trachemys will be able to learn how to hide from them.