to give a stupid example of a rounding error: on a test, the student is asked to calculate the circumference of a circle with radius 6.2. You personally did the math with π rounded to 3.14 and calculated 38.936, but one of your students rounded to 3.14159, and because of that their result is 38.955716.
Now, I doubt any decent teacher would discard this result as wrong, since the math itself was correct. However, what if this calculation was part of a much larger series of calculations for an academic paper, and the resulting rounding error throws off the entire result? It's easy to just come out and say "if you round X to 15 places instead of 14, your formula makes the English channel 10 meters wider" or "you rounded to 5 places, but if you round Y to 6 places, your result is no longer statistically significant", but it just seems like such a cheap way to give feedback for academics. Another example: "by rounding X to Y+1 places (or Y-1 places) in our formula to determine whether an event happened, we managed to shift 90% of our test group from 'happens 25% of the attempts' to 'happens 75% of the attempts'". It's an extreme example, but something like that
I know that such a remark can be seen as a meaningful one since it's a viable concern, but it's still quite a nitpick, and there's probably a reason why X was rounded to 14 places. Still, I can't help but think that a formula should work regardless of how many places you round X to.
If an academic paper you are reviewing could change result or even be invalidated due to rounding differently, how should that be handled in a peer review?