What are the aberrations of an SCT? And how can they be eliminated?
The primary aberration present in a Schmidt–Cassegrain telescope is spherical, due to the primary mirror being spherical in shape; that causes light at the edges to have a different path length than light at the center, and thus a different focal point.

The image above, from Wikipedia's "Schmidt corrector plate" webpage, shows an exaggerated corrector; they are actually much flatter.

The secondary aberration is coma, though this is present to a much lesser extent. Coma is a spherical aberration from rays that come in off-axis. Coma shows up as little off-axis comet-shaped blobs that point inwards towards the center of the field and get bigger as you look towards the edge of the field of view. 

Persons wanting a lengthy technical and mathematical explanation will enjoy reading sections: "10.2.2. Full-aperture Schmidt corrector: Schmidt camera" and "10.2.2.4. Schmidt-Cassegrain telescope (SCT)" of the https://www.telescope-optics.net/ website.

Recent improvements in the design are offered using aplanatic flat field Schmidt-Cassegrain optics. Here's a screenshot from Celestron's video showing the difference between a standard versus aplanatic Schmidt telescope design:



The competing system from Meade is called Advanced Coma-Free (ACF™) optical design. Claiming also to offer coma-free pinpoint star images and flatter image fields while reducing astigmatism and eliminating diffraction spikes. 

The website forum "Starry Nights - Cats &amp; Casses" compares Celestron and Meade.