I think I've seen a couple bugs with the Save & Resume functionality.
The first one I don't remember how I did it, but I had it saved at some point in Finding Mice and then turned the Auto Save off. From then on, there was a ghost bike just sitting there at the point I had saved previously. It didn't move, it was just there (the regular ghost bike worked fine, there was just a new gray bike sitting at that point)
The second bug happened on the new levels (Frostbite). I hadn't completed the level yet, but had the Auto Save on. (It was still on from trying to finish The Climb ) It saved right in the middle of the level and then I finished it. I turned the Auto Save off and then tried to finish the level again, but every time I crashed, it would start me in the middle of the level again. I would click on restart but it would still start in the middle. The only way I could get it to start at the beginning was to go to another level and then come back to Frostbite. Once I finished the level without the restart the problem seemed to go away.