Since the floor "flatness" problem is in the basement, and assuming that the "slope" is correct for flooding drainage, washing machine overflow drainage, water heater breaks drainage, second floor toilet pipe breaks drainage, (I've had all four!) ... then consider just demanding the contractor add a self-leveling concrete/grout on top of the bad floor slab.
By the way, even without a drain or sump pump, it is easier to mop up/suck up water from a wet basement if there is a definitive "low spot" (near the washer or water heater?) that collects water. But a floor where the bed needs to be shimmed into "level" ? No. Don't accept it.
I bought the house used, and my basement slab started with a bad slope similar to your case. The spare bedroom in the basement could not be used without propping up one end of the bed so it laid flat. Get it corrected, even if you only allow him to pour a floor leveling grout. See a carpet or wood floor installer.