Um...
(Note to self: use cheats or something, not play through the entire game just because of something telling me a room I recognize is wrong.)

I'll be honest here: I thought I recognized this from dungeon 4 and I said Link didn't use the slingshot graphic, but I was wrong on both things.

That said, in the final the slingshot is blue. I'm certain the hyperslingshot is blue too, though that very clearly is not it.
I also was unsure of the blue Ropes (snakes), but indeed, all of them are green.
The room does look very familiar, but I give up on trying to find it. Closest is this from dungeon 3 which shares the graphics at least.

 
On the other hand, now THIS is more of a comparision. The upper path is narrower, the rolling thing graphics are different, and it's missing a pair of torches in the southern wall.
 
As mentioned already, the tree is never like that. While there are similar overworld areas, it could be pressumed it looked vastly different at a point, so that place doesn't exist anymore.
Another curiosity is the ledge. In the final version, vines grow along those markings in the wall in summer, and you can only jump down them in the other seasons-- none of them have a barrier like that on top of them.
Another thing of interest: Dimitri doesn't open the mouth normally when you aren't riding him, so this would've been a cutscene if anything.
 
Moosh jumps differently, as noted.
 
This one was pointed out already too. Sorry for the filter in this one!

Now, this one is pretty interesting. First and most obvious, the dungeon graphics look completely different from any in the game: They walls aren't just 16x16 tiles, the door is very different, and none of them have borders like that in the final game. Comapre:

Less obvious is that the square block is halfway aligned with the door, indicating that door occupied two tiles.
There is nothing in the final game like the thing at the right. There is again, a door you have to burn, but it looks nothing like that.
The torches are also different from the designs in either game.
 
Clearly redesigned. Sign is now standing on land, north path got blocked (and instead an underwater tunnel was added) and the house got relocated.
The guy never is angry outside his house like that.

I don't quite understand what's going on here, but it seems Link is just damaging an enemy with an Ember Seed. In the final game, an enemy hit by them is entirely set on fire-- not hurt by running into the fire as this seems to imply.
As for the area itself...

While this is an strech, the layout does match the screen exactly. There's no other place with small trees like that either.
In any case the overworld seems to have been heavily redesigned at a point.

As mentioned, in the final game there is no such giant chicken at all.

The house and area looks very much like this, but could've been anything anywhere really.

The sole place that comes to mind is Hero's Cave (hard), but I don't think something so simple would fit there, so I'll say this room doesn't exist. Also the torches are slightly different.
Oh, and there is another small oversight there...
Link is holding his shield with the wrong arm. :V
(and blue snakes, but we already talked about those!)

I still have nothing on this one. Again, looks like something in Hero's Cave or perhaps just a random cave.

Along the rest of the overworld, this place simply doesn't exist anymore, nor there is really any place it could've been, either.

That said, there is a house here when you meet Ricky, and it does have a pool inside for some reason, but that's just silly speculation.
Also, while it could've been discoloration, if you look closely Ricky's gloves are red (as they are supposed to be anyway), they are part of his sprite in the final.
Too bad these games are tile-based unlike Link's Awakening (or so I think), and don't have the old room designs underneath, it could've been pretty useful for context here!
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