Actually, your two problems could be related. If the front action screw was tightened down after the middle, or rear one the action might not be pulled tightly back against the recoil shoulder in the stock. That would also leave the floorplate slightly forward causing it to not latch up tightly. To check this make sure the gun is unloaded, and secure since the facory sometimes tightens the heck out of the middle action screw, why, I don't know?
Anyway, assemble the gun, and run the three screws in until they seat, but are not torqued. Snug the front screw down, tighten the rear one, and just snug the middle one. Now torque the front one really snug, and give that a try. The idea is to make sure the action is seated rearward, but not to bend the action by overtightening the front screw first. The 60 degree screw in the Rugers works really well but can tip the action forward if it is tightened too much first.