Update 12 Apr 2017: An update has been released that resolves the issue.
Original post 06 Apr 2017:
We have got good news regarding Xbox save/load issues. These issues have been causing many of you to receive errors when attempting to load saved games on Xbox One. We think we have identified the problem, have worked out how to resolve it, and are in the process of a preparing an update for release.
Even better: Existing saves that are suffering from this error appear to be recoverable. The underlying problem was not, thankfully, corruption of the saved game data. This means that if you have a game that currently will not load, it is very likely that you …Read More...