Okay, time for another lengthy post.

I'll try and work on every point this weekend. Hopefully that will result in an fixed demo sunday.
This is not supposed to happen, right? It happened quite frequently to me and got pretty annoying. I'm playing on Vista, does that matter in any way?
No, it's not. Vista is pretty hard on games (I couldn't even play this game when I first got it myself) but it is Vista compatible. There is a feature called freeze when the game looses focus. I've enabled that so it may be fixed now. Beyond that, there's little I can do for you.
You should be able to close menus with the keys you use for opening them.
Why didn't I think of this. Excellent suggestion.
It would also be nice if you could pick up things like rupees with your sword.
I was a little hesitant about this. Since the engines are done I just implement it. It isn't that much trouble to remove again when I don't like it.
Pots should have square collision in my opinion. If you were walking against a row of pots you could get stuck between two pots. I mean, you could still move out again, but square collision would be better I think. You couldn't pick up pots either, could you? But you probably plan to add that anyway.
The last responder suggested square object masks. I'd go for almost square, perhaps 14x14 with very slightly rounded corners, since making them slightly easier to walk around is a nice touch. As long as it still feels like you're playing Zelda, why not improve the formula by a little bit? But getting stuck between them (which I didn't know about) and having trouble picking them up are significant problems.
I don't believe you really got stuck as in image over image. I'm that confident in my movement system. But it is true that walking in between two pots can make it feel like so, depending on which movement arrows you're pushing.
I'll go with goodnight's idea on this one. A square mask would not feel right when you walk around a stand alone container. If the current masks are too rounded, I'll try and find something in between.
On a side-note. Picking up containers can be done using different masks that walking collisions. I still haven't found usefull
pick up animations for Link (the ones on spriter resource are terrible), so maybe it's time I posted a request on this forum. After I get those I'm going to make Link able to pick stuff up.
Another thing was no knockback for Link, but same as above, I think.
I'm not really sure what you mean. Knock-back against walls, enemies or something else. I guess I should add knock-back from enemies, but I'm not really sure how it was done in the original. Did it stop your movement every single time you hit an enemy?
Also I found that the 'Royal Shrine' text vanished too quickly to read, if you aren't prepared for it.
No problem. That's an easy fix.
As I recall mentioning (though maybe I didn't), I hadn't studied how/when enemies respawn. I'd suggest respawning them after traveling to a certain number of other rooms, rather than just when changing Game Maker rooms, IF the dungeons are rather large. Walking around through large floors with all the enemies beaten could get boring. A thought just occurred: it would be neat to actually SEE them respawn via some magic power, rather than just being there when you walk in.
Also consider the overworld; most if not all enemies respawn when you change areas.
Can't argue with that. This is somewhat of an hefty order though so it may take some time to implement. As for spawning enemies; I do want to add bones on the floor that turn into skeletons, but thats for the second dungeon.
With "target location" transitions, yes, extending the target just a bit might be the best fix, but he already seems to hit the target location a few pixels farther than expected, so it must be some other kind of bug. It was a one time occurrence for that door, but Link went back and forth a good 8 times or so before I freed him. It was the door between the room just after the 1st key, and the room to the left that's just a horizontal bridge with 3 pots.
If you're using division by frames to control Link's movement during the transition, then perhaps it was a perpetual rounding error. I'm not sure how your walking code works, but if it allows Link to be at a non-integer (x,y) position at any given time, then I'd suggest also rounding off his position before the transition begins.
This just in: I reenacted the bug by dashing at the upper part of the doorway so that Link passes through but still makes the collision noise. Took many tries but I made it work 3 times. Perhaps since Link is supposed to bounce back, the target position ends up getting pulled back a bit.
Also, where the 9 pots are just above that door, sometime in the midst of cutting them up and pressing D (I think) repeatedly to get infinite blue rupees out of one, Link's sword somehow got moved an entire 2 blocks to the left and 1 down. It stayed that way through every movement until quitting.
I haven't been able to recreate this bug but I did find some other really messed up things. For example, releasing your sword while doing a transition gets you stuck. That makes me wander what else I've missed so far.
Anyway. The story about rounding won't work. This routine is a stand alone from normal movement, making it easier to fix. It's just the Link objects moving from A to B with walking animation. The starting location isn't rounded but the speed isn't either. So moving left for A to B should make that in the and B is speed*pixels left of A, because speed/number_of_frames*number_of_frames = speed. If there is a rounding error it's so small it won't matter since movement is at least two pixels farther than needed.
The collision bit might be a reason but I have no idea how you managed to get it.

When falling back through the air Link doesn't react with transition objects.

I'll add in a line negating it, regardless. Let's hope that's the solution. You're a good glitch finder it seems.
The continues rupees is something I already found and fixed myself. At least that's what I thought. What demo where you playing when you got that? I don't suppose you could put something up on youtube or something?
The two sounds are supposed to play simultaneously. If you've got an emulator, try disabling the first 6 sound channels to leave just those two. #8 is the one I mainly hear, and #7 is the one I can't. It's like a quieter version of the beam-shot from the sword.
Sorry, no emulator. I'm using memory and youtube.
Now for some new info:I'm working on customizable controls, but I'm pretty sure not everybody is going to like the menu. The point was that I wanted one screen to change all your controls, since scrolling looked dreadfull. As you move next to an action the title mentions the button associated to that action. It then switches back and forth to explain which button needs to be pressed to if you want to change the button. It's still in progress but I'm curious for your input.
ENTER, SPACE and ESC are standard buttons for confirm, confirm and cancel. These can't be changed. I'll also an automatic save feature for the controls.


Update:
Nope, didn't finish enough to justify a corrected demo by today (found a new appartment this weekend). I still need to add the "respawning" enemies. The rest is done, including the customizable controls. While I'm at it I'll also work on a global saving system which is completly new for me. And, if someone helps me with my sprite request, I should also be able to do the "pick up and throw" mechanism in about two or three weeks depending on free time. That should be enough for the next demo.