I have encountered situations where irregular rounding became solvable but annoyingly problematic to detect / calculate, in the LANL Earthquake dataset on Kaggle, it had a column with samples and a column with (incorrectly incrementing) sample times that were rounded. In order to create a corrected column, I noticed quite a lot of irregularities in the python rounding (or the underlying mechanism)

I also consider simultaneously deterministic, fast, portable rounding or binary formats to be important for decentralized delegation of computation, say a TrueBit style platform:

https://people.cs.uchicago.edu/~teutsch/papers/truebit.pdf