Facial recognition is something humans are known to be better at than computers, and identical twins throw off humans all the time.

Even when computers surpass humans at this task (probably not that far off) they will likely have difficulty with identical twins because of how they do facial recognition. At the moment computers do it by identifying points that correspond to the geometry of the face, like nose, eyes, and cheeks. These are all features that would be similar between twins. Usually humans can differentiate twins by fatness, scar tissue, hair style, etc. Not something that can't be overcome, but also not something common with current approaches.

Problem solved: We'll just add scars to twins' faces to distinguish them. /s

I don't know how they wouldn't. Hell, genetically they are probably similar enough that a DNA test can't tell the difference.

Actually DNA tests exist that can tell apart twins.

Is it a specific test, or all tests? If there is a story exploring this, I'd be somewhat interested in reading it.