Motion Paths
For some reason, Maya makes an addDoubleLinear when you attach an object to a motion path, and it connects it in a way that causes a cyclic dependency. You don't actually need this addDoubleLinear node.
To get rid of it you can shift+MMD the motion path node and the node of the object that's attached to the motion path, this will open up the Connection Editor. On the motion path node side, expand 'allCoordinates' and on the constrained node expand 'translate'. Now connect the 'xCoordinate' from the left to the 'translateX' on the right. Do the same for Y and Z. Now you can delete the addDoubleLinear node.
To get rid of it you can shift+MMD the motion path node and the node of the object that's attached to the motion path, this will open up the Connection Editor. On the motion path node side, expand 'allCoordinates' and on the constrained node expand 'translate'. Now connect the 'xCoordinate' from the left to the 'translateX' on the right. Do the same for Y and Z. Now you can delete the addDoubleLinear node.
Skinning
Make sure to remove unused influences, limit max influences and prune small influences to improve rig performance.
Profiler
The profiler can locate performance bottlenecks in your scene by recording and demonstrating in a graph the amount of time that each process consumes.