Update: As of 1.33 a functionality like this is available in stdlib (at least for simple type). For iterators you can use iterator.map(Result::transpose) or iterator.map(Option::transpose) (thread).
Turn Option<Result<O, E>> into <Result<Option<O>, E>> and the other way around.
Also for Iterators and potentially other types.
Feel free to submit PR for other types where this operation makes sense.