Unfortunately numerical stability is a very complex topic and depends entirely on the use-case. Sure, there's your usual suspects like subtractive cancellation

Unfortunately numerical stability is a very complex topic and depends entirely on the use-case. 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.