There seem to be some dependency on which fonts are used. Trying out most of the fonts installed on my iPad, hardly anyone displayed correctly in Adobe Reader. However, all except Heiti and Zapfino were readable. Heiti and Zapfino displayed as dots: ••••
One font actually displayed as it should, and that was Apple Gothic. It is a mystery why that one of all fonts worked.
Most other fonts displayed as Adobe Sans MM. To get a consistent layout, you can try using Arial or Helvetica in Pages for iPad, as they also are sans serif fonts. You can also try Apple Gothic.
It is nevertheless good to validate the file in Adobe Reader. The final display may depend on your system or the layout of the document.

A list of embedded fonts in Adobe Reader. File > Properties > Fonts.