If the problem of gaming the system could be gotten around, something very similar to internet comments could work - anyone can post a public review of anyone's work, in which case reputation would become the currency. Successfully criticizing someone with higher reputation than yourself would gain more status than praising them, but also come with more risk. It would also make it a lot less meaningful to get those 'not new ideas lol' comments that others on this thread have complained of.

I quite like the fact that whatever someone says on the internet now, the first comment is usually the best-argued counterpoint. It seems like a dynamic that could be brought to science quite well. I may not have the time to parse an entire paper in a field unfamiliar to me, but if I come across it and the top comment is 'there's a math error in table 6 that throws paragraph 4 into doubt', I can certainly verify that for myself. That sort of 'peer' review would make science much more accessible to the interested layperson.