However, as soon as they described the actual solution I felt somewhat let down.
1. Reducing the input to 80x80 images is likely unnecessary; it removes some of the most important features (number of thorns, blemishes) from contention. If the issue is computational cost (and therefore training time) you might consider using cloud GPUs. However, a network with multiple "towers" (like Google's Inception model) could conceivably allow for evaluating the sorts of aspects that require higher resolution relatively cheaply (one-or-two convolutional layers with pooling and then a fully connected layer) along one pathway, while a different tower (with more layers or more units per layer) processes the resized images.
2. If the network used was just a modification of the MNIST one, then it seems like it ignores the ordinal nature of the problem. If cucumber quality can be ordered, why not use a regression model instead (or maybe regression along multiple criteria, like straightness, bumpiness, thickness, etc.) instead of treating each class as if they were completely separate?
3. Why not release the dataset? I have GPUs, the necessary background, and a few hours to try out some models. I also have a heretofore unrecognized yen to use my models to generate images of the ideal Japanese cucumber, so I'd be willing to do it for free.