I don't think a lot of people understand how little rigidity many machines have. There can be looseness in the linear bearings, looseness in ball screw nuts and end bearings, looseness and stretch in timing belts, flex in the machine frame, flex in the moving cross members, looseness in the spindle bearings, flex in the spindle, flex in the toolholder, and flex in the too itself. This explains why industrial machines weigh thousands of pounds.
An interesting experiment that may help many of you get better results. Place a dial indicator on the table and against the tool in the spindle. Press on the tool with you finger and see how far the indicator moves. If you take the torque rating of your spindle motor and convert it to force at the radius of the tool you want to use you can then push on the tool with that amount of force to see how much deflection would occur at maximum load. Moving the dial indicator up onto the spindle will remove tool deflection from the measurement. Moving it onto the spindle housing removes the spindle deflection. Moving it on to each axis shows the axis motion.
The axis themselves may see much larger forces as they accelerate and decelerate in each direction. You can estimate that force from the motor torque rating and the gear ratio applied to drive the axis. Pressing against the axis with that amount of force will show how much deflection there can be in a rapid turn around a corner. If you move the dial indicator to show deflection in one part to another you may find there is a real weak link worth fixing.
Years ago I built pneumatically actuated bagging machines and a thermal printer mounted on the machine printed very poorly due to vibration. Everyone suggested changes to fix the problem. Using the dial indicator as above I isolated the bulk of the problem to one frame member no one suspected. Beefing that up solved the problem very simply.