NB Scratch 3 may show same problem but solution differs - move the whole costume in the editor to reassign the centre. Just press green flag to start. See inside to look at the costumes - you could try to fix the problems to make sure you understand what's happening. (Don't bother saving as a remix, there's no point, just work on a temporary copy of the project.) All the problems can be fixed by changing costume centers.
I've been responding to a few requests for help in the 'Help With Scripts' forum recently and one common problem is with costume centers not being set correctly. This project shows how the problem can affect things and shows where to find the option to change costume centers. Added rotation example Oct 2015.