My Advanced GT mount acts strangely - slow slewing or going off the object when it’s looking high in the sky.

You are probably looking at an object or objects near the meridian. Because of the way the German equatorial mount is designed, motions near the meridian are different than for other parts of the sky. The scope’s actually engineered not to track across the meridian.

You need to stop the slew with any one of the arrow (direction) buttons and wait until the object has crossed the meridian.

Updated 12/27/13