I have the Kobo iOS app and I have the same problems. I tend not to sync, but rather remember where I left off and go forward to that point manually.
I also have the discrepancy in amount read, where my KT gives me an accurate percentage and the iOS app is a few percentage points more. The slider at the bottom of the screen also seems to be wildly inaccurate as to where I am in a book.
I dislike the app and tend not to use it unless I've forgotten my Kobo.