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 will be able to resume playing it after we update the game.
We do not know when we will release the update. There are a few Xbox processes we need to go through before we can release. We are in the midst of working through those processes. It is quite likely that the update will be released within the coming week, and near-certain that it will be released before the end of the month.
This bug has been horrible – Both for you to have to suffer, and for us to find and kill. We’re very appreciative of all of you that have joined in to play Subnautica during the Game Preview phase. By bringing this issue to our attention now, you have helped avert the loss of saved games on release. We are very thankful for that.
PS. Bonus qoute from Max describing the bug: “The error message itself would happen if one of the files in the save game had a compressed size that was a multiple of 1024. This made it difficult for us to reproduce, since there was essentially a 1 in 1024 chance of that happening (not exactly true, but close enough). Fortunately, we did happen to get one of those which made debugging the problem possible.”