For both forms and annotations changes to be seen, the person opening the document needs to be using a PDF Viewer that supports viewing forms or annotations. The viewers built into iOS (like iBooks, the iOS Mail application, or the viewer used by applications like Dropbox) do not support viewing filled forms or annotations even though these items are part of the published ISO PDF standard. If you view these in another viewer that supports them (like the Desktop Adobe Reader or one of several other PDF Viewers available in the App Store from other vendors), you will see the changes. My suggestion is to encourage recipients of documents to open them in Adobe Reader or another reading application that supports viewing these values which are part of the PDF specification.
Others have requested the ability to "flatten" a PDF before sharing or submitting it. This is something we are considering, but there are a number of drawbacks to flattened PDF's (like inabiilty to reply to or move a comment and inability to edit form data). We're trying to figure out whether or not to add this capability. We appreciate your feedback and your request for this feature has been noted!
Were you printing from the the Mobile Adobe Reader or another application?
If you are printing in the Adobe Reader application, we're currently using Apple's AirPrint to print the PDF directly. AirPrint does not print annotations or form fields. This is an issue for which we are exploring solutions but don't yet have definite plans. Thank you for noting the problem, it helps us to understand how many people are encountering it!
Thank you again.