This is a topic that's been of real interest to me too. I've done some research and happy to share what I've learned. It would be great to have this elaborated by others with more knowledge than me.
I found a useful guide on pre-war authentication here:
http://cycleback.com/
Most of my questions have been about post war cards.
Sportscard Counterfiet Dectector by Bob Lemke is a very good resource. I picked up a used version from 1994 really cheap. As I'm not trying to authenticate modern cards, this was OK for me.
Key themes to check:
1) Pixelation in the cards and understanding the subtleties of half-tone printing.
2) Looking at the solid color areas of the card. These are generally, the facsimile signatures on the card and the solid color bars with the player/team name on them.
3) Comparing the card stock to a known good example
4) Cards that are too short (e.g. trimming)
5) Artificial ageing. I'm still learning to detect these.
5) Printing quality issues (e.g. is something blurry or less detailed than you'd expect)
6) Typos (e.g. incorrect branding, logos, text)
I've attached photos of a real 1955 Jackie Robinson and a Reprint card that I bought to learn the difference. Hopefully, it's helpful.