The dictation function is working reasonably well as long as I stay in the text field (after resetting the app as Girish M recommended above, many thanks). For some reason, when I say "new paragraph," I get two carriage returns instead of one. This doesn't
happen in other applications.
Dictation never works in footnotes, and any attempt to dictate in footnotes will freeze the dictation function completely. Dictation sometimes works in a Track Changes comment box, but more often it fails and freezes the dictation completely. (What I mean
by complete freezing is that dictation will no longer work in text or anywhere else. The app will still allow me to type, but the dictation button stops working. The only way to get the dictation function back is to close the document and reopen it.)
FrancescoCaviglia seems to find the same problem in tables that I find in footnotes and Track Changes.
In other words, there seem to be a number of dictation bugs in Word for iPad. I hope they get them worked out! At the moment, Pages remains a better choice for people who rely on dictation for productivity speed.