I couldn’t find info about this anywhere which baffles me because this seems like a huge problem. either that or i am doing something very wrong. whenever i try to select multiple layers or a group of layers and move it, there is always something out of place when im done moving it. no matter how carefully i move it there is always something distorted in some way. i tried the smooth move tool and transformation tool
When using the transformation tool please be sure that all handles are shown. It should solve your problem.
-G