I hear liquid sloshing behind the dashboard of my 00 discovery II when I accelerate on turn L or R. No water leakage under the vehicle or on the floorboard. Anyone experience this problem?

 

Your cooling system isn't bled properly. There is air in it.

Make it a priority to fix because your cooling system isn't working properly right now, and these trucks have a barely adequate cooling system to begin with.

 

do a search here for "waterfall" that is the name it is commonly called here. Tons of posts about it and generally easy to fix with one of the several ways posted on this forum

 

This sound constitutes air in the system. If you have a local import shop in your area (not dealer) I would pay them a visit and have the system pressure tested for leaks and have them vacuum system down and refill. There are different ways on this forum to bleed the system but I would stick to the Rave manual if performing yourself. May want to drain and flush system and convert to green antifreeze, less corrosive on gaskets and system.