In the following compound, there is one chiral center and two methylene groups. Why are the protons on the ethyl ester methylene not diastereotopic?
You are correct to conclude that they are diastereotopic. There appears to be a bit of splitting evident if you look closely at the NMR, but it might be expected to be very small given the distance between the ethyl group methylene protons and the chiral center. But even if the distance were greater and the resulting splitting too small to be observed, the protons would still be technically diastereotopic.