I have at least one German book that used "Schoenberg" because this was the correct spelling when he lived in the US but it is uncommon. In any case using ae, oe, ue has been an accepted way to deal with Umlaute even within German speaking countries if one was using a typewriter without them. As in the last millenium, I think it got worse with the early computers and word processors because they were international whereas typewriters usually had ä,ö,ü. It is not pretty, but not a real error. A real but unfortunately quite common error that might seem slight but looks jarring and ugly to native readers is treating the diphthong "äu" in the wrong way, e.g. Gebaüde instead of Gebäude (building). My sister recently told me that she read an american book/dissertation in art history that supposedly was pretty highly regarded but had this error all the time. It was about the Bauhaus and there is the expression "Bauhäusler" for the artists from that school.
