Not that I've found, but the missions are relatively short anyways. The game appears to autosave at the end of each stage too, so you can load back to each point in time.

There is no in-mission save. There are checkpoints so you can restart from a checkpoint if something happens in the mission that you didn't like. But you can't quit the game and restart at a checkpoint.

The missions are pretty short so it's not "annoying" if for some reason you wanted to quit half way through a mission. You would at most have to replay a few minutes.

I played 4 missions, exited, and when I restarted, it started back at mission 1. how do I continue with the next mission?

The game should auto-save after missions... The saves are stored in the Windows user's profile, so if you use another username that might be the reason. Cannot help otherwise, sorry.

That doesn't sound right. It should save the mission your on. Try running the game in Administrator Mode, I know some other games have issues with saving games when not run in this mode.

The game highlights Mission 1 when you start it up; try clicking on the next mission and see if that does it.

The checkpoints weren't bad, but the missions almost breached that "I really don't have this much time to dedicate to a single play session" rule. Almost.