I am also experiencing this - load screen progress bar stops at 99%. I have tried 4 times with the same result (though once it stopped at 98%).
Game should be loading into the Geoscape. There is a mission on its way to a crash site when I made the save.
When the progress bar reaches 99% the loading music cuts out and another track starts, I think this is the Geoscape soundtrack.
I have left it in this state for 10 minutes with no change.
Update: I managed to repeat the error. Started a new game, did one mission, saved and tried to reload. Similar result, but stopped at 90% this time.
