The Schmidt-Cassegrain telescope is amazing! It is compact, suitable for astrophotography ,and it requires little to no collimation. However, the SCT has some inherent optical issues. What are they? What are their causes? and how can they be eliminated?
Astigmatism. No way to eliminate in SCT. Reduce it with proper fixing of every optical element. Astigmatism is only eliminated with 3-mirror scheme.
Curvature of field. No way to eliminate in SCT. You are forced to use so-called "field flatteners". If kept in good range, does not hurt, if you are not going to do astrophotography (which with SCT nobody does).
Chromatism. No way to eliminate residual chromatism from corrector.
Corrector blur. No way to eliminate low-quality corrector aberrations.
Overall, SCT is good consumer design (together with MCT), providing nice compromise for all aberrations for astronomical observations (not astrophotography).
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 & Casses" compares Celestron and Meade.