Note mirrioring makes my charictor sprite move slighty any way to fix that?
Make sure the Origin Point on every animation/frame for the object is centered horizontally. If the Origin Point is further to the left or right, it will cause it to jump around when it's mirrored.
EDIT: If the object is moving up & down. Then make sure the Origin Point is at the same location on the Y Axis for each animation/frame. To make it easy, you can right click the Origin Point in the Point list, and select the option to have it apply to every animation & frame.