Stars shift or grow tails

This is known as coma. If your target is changing shape when you focus, then your telescope may be suffering from astigmatism – that’s when one or more of the optical components are not perfectly symmetrical. It can also happen when there’s a bit of pressure on the optical components.

Solution

You can buy accessories to correct coma, but you might find that these are quite expensive. If you own a reflector then you should check that nothing is pushing down on your instrument’s mirrors and warping them slightly. Alternatively, if the astigmatism is severe, you should replace the troublesome component. If your instrument is new, ask for a refund.