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99.3% is pretty good for a one hour lecture that begins with a single-layer network.

What is the human accuracy on this data set?

more interesting question: if some of those "digits" are so hard to recognize even by humans then how can we ever label them with the one true "correct" answer?

Do we know a person who draw those digits and ask "what artist had in mind when making this masterpiece" ? And even then someone might have been trying to draw the "2" but end effect looks more like "3".

I think that some of the test cases simply don't have definitive answer and trying to reach 100% accuracy is just misguided effort.

Another interesting question is which approach most closely matches the errors made by humans.

I wonder, is there a good reason why these accuracies are reported on a logscale by convention (say, as power of 2 from 50%)?

To make even small difference look bigger, cause even a 0.1% improvement over previous best result is considered big deal.