Meade 114 EQ AST tripod vibrations
Also, tightening the thumbscrews for the Latitude lock, Azimuth lock, RA lock, and Dec lock causes the mount to turn slightly as these locks are snugged down.
This is my first use of a telescope so maybe these issues are normal. I just would like to make sure I'm not missing anything that could make observing easier and more fun.
Part of the difficulty you are experiencing is from the way the 114EQ-AST is attached to the mount. It uses only one attachement point compared to the full scale cradle of the standard 114EQ-A. With the lighter weight mount, even the slack you take up when you tighten down the locks is translated into more vibration.
You can minimize this vibration by keeping the magnification down, of course. If you are observing on a hard surface, it will also help to set up on a lwan or other soft surface. Lastly, you can try adding some weight to the telescope (tape some scrap metal on the tube- a little will go a long way here. Don't overdo.)