I would have to research more on their data and the data available elsewhere, but if you want me to shoot in the dark:
Due to time constraints I'd look at an unsupervised algorithm, especially if the data is appropriately categorized. I'd look at a classification algorithm to determine whether it is coherent and supports a round earth - perhaps even a competitive classification algorithm. I'd likely use an open library for doing this, and pipe it into that.
Alternately, we could take a non-machine learning based approach. Taking the National High Altitude Photography data set which is meant to cover the contiguous states at 40,000 feet we can extrapolate how much overlay should exist between the photos given a flat surface photograph being placed on top of a globe. If this value differs, we have solved a problem.
The bulk of the work is in finding "good" data.
Another idea: take the Landsat Image Mosaic of Antarctica (LIMA) dataset and compare it to newer and older attempts.
Another: cross reference attempts to map the coast of the antarctic over years and show inconsistency.
Another: Look at their landslides by country data set and see if it correlates with coriolis effects.
So to answer you:
1) Find a good data set
2) program something to read it in
3) write something to analyze it