I just had 4 flats in 4 rides, and I could NOT find the problem. Finally, however, I did. It was inside the tire, but barely visible...one little thread or wire of the tire was not perfectly flush with the tire...it just barely poked up, and only when I flexed the tire a certain way.

After I found that spot, I thought that surely booting it would do...but no. Another flat. Got a new tire today.