After some quick internet research, I tried a couple of suggestions.
1) I took a regular eraser to the smudges. Sites suggest rubbing only in one direction, but I went crazy going back and forth. Most of the marks came off with just the eraser.
2) Next, I took a q-tip dipped in rubbing alcohol and wiped at the remaining scuff marks. It totally did the trick. I also used it on some scuff marks that I hadn't erased, and the alcohol actually seemed more effective than the eraser.
3) I used tissue smeared with some petroleum jelly, and it was just ok. Even if the petroleum jelly is not used to clean up the scuff marks, it's an excellent way to polish up the patent leather after rubbing off the scuff marks. It brings back the shininess to the surface.
Here are some other methods that I didn't try:
*Use non-acetone nail polish remover with a cotton ball to polish off the marks. (I get really paranoid that using nail polish remover would damage the color or surface so I opted out of this recommendation.)
*Mix 2 tablespoons of baking soda with warm water on a cloth. Scrub the stains.
*Use dish soap and water on a cloth to rub the scuff marks.
Tried any of the above solutions? Do you have your own?