Whenever I export a design as a PNG, the text on it looks all funny:
It reminds me of when, in Photoshop, you mess around with the ‘font smoothing’ bit of the character panel.
Except in InDesign, there appears to be no settings like this… nor when I export.
The only thing I can think of would be the anti-aliasing option, but that is checked anyway?
The easiest solution is to export png in higher resolution and later resize images in Acdsee (using batching) or Photoshop (using actions). I use this method constantly because many fonts has bad hinting instruction, which are causing x-height jumping (like in your sample).
Another solution is to convert all text into outlines before exporting.