I'm scanning a lot of cards and I'm using Photoshop's automated "crop and straighten" function to auto rotate and crop them after. But the result wasn't very accurate as some of the sides of the scans were clearly cropped off. I think maybe that has to do with my cards having rounded corners? What other alternative program do I have on this?
I don't have an alternative for you but this is too long for a comment...
Speed is obtained by consistency. Getting rid of the auto crop and utilizing the same crop per layout will drive the most consistent, fast results. However, this requires that your initial files be exactly the same.
If you are using a camera as a scanner by photographing images, this means that you need to make an easel so that you can place the card in exactly the same spot. Telling Photoshop to crop at exactly x,y coordinates after that is fairly simple.
If you are using a flatbed scanner, make an "easel" by using masking tape so that you can scan multiple cards at the same time and ensure they are all in the same spot. Use a Photoshop Action to watch you make crops off the first and then apply that action to the rest.
If you are simply throwing the cards on the scanner, or attempting to lay them out by hand with no sort of easel, then you are not being consistent. This will hurt your speed. There may be a computer program out there that can overcome your rush to scan - but really this boils down to work smarter, not harder.