Here are a few common causes of trailing or distorted images, along with their solutions.
The stars appear to have moved in short arcs. This is field rotation - the apparent rotation of a celestial object in the field of view of a telescope during the course of the night. Objects in the image will move in small circular segments or arcs. The autoguider is continually correcting the motion of the mount in declination. It happens when you are using an altazimuth mount or a misaligned equatorial mount. In these cases, all the stars will appear to move around the point or star that is being tracked. Field rotation will occur unless the mount is exactly polar-aligned to counteract the earth's rotation.
If you use a polar axis finderscope for polar alignment, then you might think you had accurate polar alignment, only to see field rotation in your images. In this case, double check that the finderscope and its reticle are indeed aligned with the mechanical axis of your mount so as the mount moves in right ascension, there is no movement at the center of the finderscope.
All stars appear double. This means you bumped the mount, tripod or camera during the exposure and shifted the imaging field of view.
Stars are trailing in right ascension (RA). This means the mount has periodic error that the autoguider isn’t compensating out. Use periodic error correction (PEC) if it is available on your mount. Otherwise, the mount and or power supply are possible sources and may need to be fixed or replaced.
Stars are trailing in declination. Adjust the autoguider settings to reduce the aggressiveness. Turn down the guiding speed. Also look at the turning down anti backlash settings of your mount.
The stars are oblong. Differential tube flexure between the guide scope and imaging scope is the most likely cause. Tighten rings and increase the rigidity of your setup. Piggybacked cameras with telephoto lenses may be slipping and or need more support (front-end under the lens) or to be tightened better to existing support.
Stars are trailed on images taken with Schmidt-Cassegrain telescopes. This may be primary mirror flop (also called mirror shift) caused by moving mirror focusing in the telescope design. Use mirror clutches/locks and avoid meridian-crossing exposures that change the direction of the force of gravity on the mirror.