There is a bug in Logos 4.5 SR-3 for Macintosh that will cause sync to show an error icon. We are aware of the problem and will be releasing SR-4 to fix it.
The bug causes a failure while syncing preferences; all other documents (Notes, Highlighting, Layouts, etc.) should continue syncing in the background even though the error icon is displayed.
This is unrelated to the sync problem in iOS.