In fact, the general rule that creatures about to be forced into damaging terrain get a saving throw to fall prone and avoid going into the damaging terrain implies very strongly that the general rule is that creatures can take damage from being forced into hazards or zones.
Hm, that rules as I understand it is for when a creature is about to be pushed off a cliff with forced movement; the creature can make a saving throw that represents the creature grabbing hold of the ledge at the last minute. Shouldn't apply to Stinking Cloud.
Besides, the rule is not about "damaging" terrain which is a generic term without any meaning in the rules, it's about "hindering" terrain which is a very specific type of terrain, one which Stinking Cloud is not. So extrapolating something from hindering terrain rules is neither less nor more valid than extrapolating it from difficult terrain rules... except the extrapolation from the difficult terrain rule is backed up by the Opportunity Attack rule. So I'm going with that one.
There is no need to keep track of whether or not a monster already took damage. If the creature was pushed into the cloud, it takes damage from entering the cloud (one of the explicit conditions under which the spell deals damage). If that creature then begins its turn in the cloud, it takes damage again since it meets the condition for taking damage--begins its turn inside the cloud.
Hm, I guess I could be persuaded by this, except for the fact that it creates an automatic double-hit. Even if the in-out-in-out thing isn't abused, the creature still 1) takes damage when being forced into the cloud and 2) unavoidably takes damage again upon starting his turn. I don't really like the sound of that.
That said, if official word from WotC comes down about this, I'd be happy to make the change.
Edit -> I guess what gets me about this is that if the Obscured Terrain rules aren't for things like clouds and fog and smoke... then
what the heck are they FOR?? I mean that's what you've got: partial darkness... stuff like branches and leaves... and stuff like clouds, smoke, mist and fog. That's it. Those are the obscuring terrains. *There's nothing else* to use those rules on.
Then I've got page 62 of the DMG giving me fog and mist and pretty much the only example of what obscuring terrain can be, but then we have the power itself not mentioning that at all and making reference to line of sight, where the PHB page 273 cheerfully tells me that yeah clouds are also one of the things that block line of sight.
It's easy to make one interpretation and feel that it's clear-cut and obvious if you look at only one part of the rules, but look at the whole thing and it's pretty apparent that something isn't right.