In the upper rear right corner bracket is a stepper motor.  The motor shaft of that stepper motor is coupled to a rod and belt pulley that moves the printer in the X axis.  If this coupling is loose, layer shifting can occur.

To check if this coupling is loose, jam your finger up into that corner bracket between the bracket and the coupling.  This should lock the coupling in place and prevent it from turning.  At the same time, using your finger will allow you to feel if the coupling is moving.  With the coupling locked in place, move the hotend assembly left and right on the rails.  It should be unable to move since the coupling is locked.

If however you are able to move the hotend assembly while you verify feeling with your finger that the coupling is indeed not turning, this indicates that the coupling is not securely attached to the stepper motor shaft and/or the rod.  If this is the case, you'll have to look underneath at the coupling and turn it until you see the set screws to tighten.

The Y axis motor and it's coupling can also be checked the same way.  That motor is housed in the upper rear left corner bracket.