I'm having trouble saving with my XBOX 360 with Dead Space 3. I'll play a lot, then I'll save and quit. When I come back it puts me way back, nowhere near where I saved. I tried clearing my cache, and it seemed to happen after I did the update on line
The game saves your mission progress when "saving progress" indicator is displayed on-screen (there are also checkpoint-related saving notifications). If you quit the game when the notification has just been displayed your character resumes from the exact same point.
I only have experience with the PC version. Saving behavior may have been tweaked in updates and the existing answers may have been correct at the time of posting.