Same here. Started immediately after the XB one app update, and not the server update. Was watching a series without issue, app updated, and following that, the same series and episodes were unwatchable for more than a minute or so at any rate or transcode setting. This was in the same evening.
That particular series is the only one that I have had issues that bad with. Other series will play, but invariably the show will pause and show the buffering animation at some point mid-way through the file. It will eventually boot me back to the episode menu. If I hit play again, it will bring up the start over or resume dialog, and the select button then will not work on the resume button. If by exiting the episode and going back I can finally get resume to toggle (rarely), then I get a problem playing file error. If I force close the app and restart it, it will usually resume playing ok, and most of the time will make it through the episode. It is guaranteed to happen again on the next episode.
I have to agree with others in this thread, that it makes the app extremely frustrating to use, if not entirely unusable. I checked the forums the night of the release, to see if others were experiencing similar issues. There were threads describing the same issue even then, and so it is a bit frustrating that this seemlingly widespread problem does not yet appear on the “known issues” post.