Proposed resolution:

Change the signature in [time] and [time.duration.nonmember] to:

template <class Rep1, class PeriodRep2, class Rep2Period>
    duration<typename common_type<Rep1, Rep2>::type, Period>
        operator*(const Rep1& s, const duration<Rep2, Period>& d);

In [time] and [time.duration.nonmember] we have:

template <class Rep1, class Period, class Rep2>
    duration<typename common_type<Rep1, Rep2>::type, Period>
        operator*(const Rep1& s, const duration<Rep2, Period>& d);

Everywhere else, we always have <rep, period> in that order for a given type. But here, we have Period and Rep2 in reverse order for <Rep2, Period>. This is probably of little importance, since the template parameters are seldom spelled out for a function like this. But changing it now will eliminate a potential source of future errors and confusion.