I believe your question has been addressed in the Adobe Reader for iOS forum in this thread:
The relevant text:
"Some forms do not display correctly in the Desktop Reader if field highlighting is enabled. This is something we're actively working on, but you might try disabling field highlights by clicking on the button in the purple bar at the top of the Document in the Desktop Reader to see if that helps."
Hope this information helps. If this does not remedy your problem, please let me know via email at firstname.lastname@example.org.
The form in question appears to be a Static XFA Form that was authored by a tool like Adobe LiveCycle Designer.
Unfortunately, Static XFA Forms are not supported by the 10.2 Reader Mobile Release (AcroForms are currently the only supported format).
More unfortunately, it appears as though you can fill these types of forms with 10.2 Reader Mobile, but as you've discovered, it doesn't round trip to the Desktop.
Filling Static XFA Forms has turned out to be a not-uncommon request for Mobile Reader so it is something we may be assessing for inclusion in an upcoming release.