Overlapping shifts could just be seen as a better hand-off. However I think the hand-off issues are probably the same that you have in any project. There's a lot of implicit knowledge. E.g. you've noticed patient X was breathing heavily, but you weren't sure if it meant something, if you see that again 10h later you might investigate, while for the other doctor if he started after 8h he might notice it for the first time, and have a similar wait and see approach.

In this case one procedural way to make this better would be to teach doctors to write up anything unusual they notice during the day, and read this list of unusual events during hand-off to the next doctor.