Why would Margot have known the key was under the carpet?

She didn't know about the key being under the carpet on the stairs -- that's how they proved she was innocent. Had she known it was there, she would have used it to get into the apartment, but as she went around through the garden, it was clear she had no knowledge that it remained hidden there.

The OP is correct. If she was guilty that would have meant she let Swan in the apartment herself. She never would have had a reason to leave the key outside.

The dramatic failure of Kelly to realize why her key wasn't working, thus "proving" her innocence to the inspector made for a good scene, but did not make sense: had she really been the murderer the keys would never have entered into it; that was part of Milland's plot, not hers. If she'd planned to murder him in her own home, she would just have let him in then staged a burglary by breaking the window. Her ignorance of the key would not have revealed anything.

Thought you might like to read my response to "Why not make a spare?" (which immediately occurred to me). Perhaps you might have some thoughts on some of the questions raised. Also, I'd wondered why the inspector did the whole "Is is this your key ... no it must be mine" routine, until I realized that he had to confirm that Tony had his key in the lookalike raincoat.

Precisely. Also, he said to Swan: "Now, this is the most important part: when you LEAVE place the key under the carpet." For someone who so meticulously thought out all the angles, if this were so important he would have told him to do what all people with hide a keys do: open the door and IMMEDIATELY lput it back so you don't forget it! This was even more important when you've just murdered a woman and are perhaps not thinking clearly and prone to forget details. And why the hell did he ask Margot, in front of Tony, to lend him his key before he left? Why focus any attention on the key if it is so, well, key? Why not just take it secretly as he wound up doing? As for those below who thought that the extra key would have left a trail back to him through registration requirements, etc., they are thinking in hindsight, since the existence of a spare key was only critical AFTER the unexpected failure of the murder; I don't think anyone, no matter how meticulous, would have covered every single eventuality such as that.

I think what the inspector was checking was whether the stair carpet was a usual place for the Wendices to hide a key. If she had used a key that was there, as in a place they sometimes hid a key, that wouldn't have cleared her.

Then again, seems like they could have checked for Swann's fingerprints on the key. Would it have been completely rubbed off placing it under that relatively loose carpet?

Interesting question. Made me think about it for a while. At first I agreed with the OP, but I guess there IS an explanation for it.

The inspector found the key under the carpet on the stairs. He had to find out if this was a habit of the couple. Problem is that if he asks them that Margot will be truly surprised and Tony will act it. The key of Margot ís the ledge key of Swann. It is logical to assume that when Margot intentionally had killed Swann she never would have put the key there. But...there was the possibillity that Margot would have used this as a "back up" plan in case something would go wrong. It could be that she had planted that key there in order to bring the suspicion upon Tony.

You could be right (a case of bad writing, although a forgivable one), and yet, the inspector probably wanted to verify if the carpet was a usual hiding spot for the couple, as other posters have mentioned. Her not finding the key prepares the final test: will her husband find it? When he does, it proves that he was the only one who knew about it, which further validates the inspector's hypothesis about him.

So that's probably a case of imprecise writing: her not finding the hidden key indeed doesn't clear her directly (as was implied by what the inspector says to her afterwards), but, rather, is a necessary step to prepare the final test with her husband. However, proving the husband's guilt does clear her even more clearly, so, indirectly, her not finding the key was key to clearing her!

Edit: The inspector's exact words: "because you were the only other person who could possibly have left that key outside". The word possibly suggests that the inspector didn't have a particularly clear idea as to why she would've left the key there, but that he nevertheless had to make sure in order for the final trap with her husband to have any validity.

Then: "Suppose I had known?", to which he answers "You didn't". The viewer may interpret this as "If you had known, then you wouldn't have been cleared", but that's not what is said. I think he simply means "we wouldn't have been able to truly test your husband and prove his guilt" (in which case she probably would've been cleared anyway, if only on the basis of reasonable doubt... unless the logic is "you can only be cleared if we find the real killer", but of course that's not how our justice system is supposed to work).

In any case, this still looks like somewhat imprecise writing/reasoning, even though it does add dramatic effect.