I found a thoughtful essay by a guy named Barry Garelick. He does a good job of dissecting the flaws in spiral mathematics, using Everyday Math's approach.

Originally Posted by EM promotional material (top) and Barry Garelick (bottom)
“The Everyday Mathematics curriculum incorporates the belief that people rarely learn new concepts or skills the first time they experience them, but fully understand them only after repeated exposures. Students in the program study important concepts over consecutive years; each grade level builds on and extends conceptual understanding.”

This does in fact make sense considering that for most people a particular concept or task starts to make more sense after they have moved on to the next level. But this phenomenon occurs when there is mastery at each previous level. ... Each previous bit of learning seems that much more apparent at the next level of understanding. In EM, however, students are exposed to topics repeatedly, but mastery does not necessarily occur. Topics jump around from day to day. ...

A casual glance at Everyday Math’s workbook pages does not reveal that there is anything amiss. The problems seem reasonable, and in some cases they are exactly the same type given in Singapore Math. What the casual observer doesn’t know is what sequencing has preceded that particular lesson...