I create a simple EntryElement “eNote” and add it to a Section. Super simple.
Section secNote = new Section ("Notes");
eNote.AutocapitalizationType = UITextAutocapitalizationType.None;
eNote.AutocorrectionType = UITextAutocorrectionType.No;
eNote.KeyboardType = UIKeyboardType.ASCIICapable;
secNote.Add (eNote);
We type in a sentence like this:

Then when I try to add the text “I Like” before “Unity” by tapping before the “U”, the first letter gets entered, but the rest gets put at the end of the text. The result is we can’t edit text.

This is a regression caused by this change. If you build MonoTouch.Dialog from source (github) then you can revert the 4cffe144f89fc9fbfe032d56e67a8583c2d641bf commit.
The same change also had other side effects, e.g. #4736, beside the bug report you filled. You should check if this affects your application (or not) to see if the workaround is better than the revert.