Honestly, I was expecting to see suggestions for testing for numerical stability. This might be a super annoying issue if the data is just right to hit certain peculiarities of floating point numbers representation.
Sure, there's your usual suspects like subtractive cancellation, but iterative methods in particular can vary quite a lot in terms of stability.
Sometimes it's due to step sizes, sometimes problems only occur within certain value ranges, other times it's peculiarities with specific hardware or even compilers. There's really no good general way of finding/avoiding these pitfalls that would apply to most numerical problems.