When our first was born we installed it and it shook a bit, enough that I thought we did it wrong so we went to the fire stations where they will check car seats to make sure they are in right and they told us there is always some wiggle to them just to make sure all the straps are secure and that it wont tip side to side, backwards or forwards.
They told us the wiggle was in case we got in an accident that the car seat would flow a little with the movement instead of jerking really hard just like you are less likely to be injured in a car accident if you are relaxed and move with the motion instead of being stiff and being jerk around hard.
Do always make sure it is secure and doesnt tip to either side, forward or backwards. Some wiggle is normal though.