That troublesome leaf

I'm afraid that there's no good, logical answer to your question. If he'd known while he was bathing, he'd have done something about it; and it's not possible he could have found out afterwards, since the only way he'd know is if someone killed him in that spot - and then, of course, the knowledge would come rather too late (!).

But. Thea von Harbou's screenplay is doing something quite sophisticated at this point. Although the film has started, like all good legends, in media res, with Siegfried forging his wondrous sword, and the narrative is being objectively told (ie, through the camera eye), by the time Mime the smith has sent our hero into Woden Wood, the point of view has changed. It is only after the adventure with the dragon that this becomes clear, but the story is now being told by Volker, the Burgundian bard. There are two reasons for this: firstly, because it provides balance with Siegfried's story. He has heard about the matchless beauty of Kriemhild from the mocking idlers at Mime's forge, and fallen in love with the idea of winning her. She, in turn, having (we understand) refused numerous suitors, hears about the great Siegfried second-hand (ie, through Volker's song), and falls in love with the idea of him. And secondly, because this allows Lang to get around the leaf problem (without bringing in the gods which feature in other versions of the legend - compare directly with Achilles, and his heel). In other words, we are being told about the leaf by someone else entirely (Volker), rather than experiencing the action alongside Siegfried.

Now, this doesn't directly answer your question, postdlf, because it would still have needed a third party to be present during Siegfried's bath/shower to see the leaf (a person whom we are not shown in the film). But it does allow the possibility of one, who has just added the information to the growing set of legends surrounding Siegfried. All we see, between the dragon episode and Siegfried's arrival in Burgundy, is his adventure with Alberich, and yet, when he turns up, he has twelve conquered Kings as his vassals, so a lot of time has clearly passed between his meeting the dragon and his meeting Kriemhild, time for all sorts of stories to have been created around him which can fill out the minstrels' ballads.

The leaf is one of these, and while it's impossible to explain how anyone knows about it, it is important figuratively, as well as being the means by which Hagen Tronje can murder Siegfried. Because for Lang, Siegfried is not perfect: his spilling of the secret regarding the seduction of Brunhilda is what brings about his downfall, and, eventually, all of Burgundy's. It seems like only a small thing, one loose word to the woman whom he loves, but it's the catalyst for everything that follows. The leaf symbolises that quite succinctly.

However, if you, or anyone else, can tell me how and why, in this version, Brunhilda dies, I would be very interested. Once she and Siegfried are dead, magic has passed from the world, and the second film is much more straightforward, and rather more naturalistic, but exactly what causes her to pass here I find very mysterious.

I'm afraid I've been very long-winded and, you may feel, not even answered your question properly, but I hope some of the above helps a bit.

The only third person we saw at the dragon spring was the bird, whose song told Siegfried that if he bathed in the dragon's blood he'd be invincible. Maybe the bird saw the leaf and then later sang about Siegfried's vulnerability to someone else who then spread the word.

Clearly Siegfried kept in communication with that magical bird, the one who initially suggested bathing in the dragon's blood and was present when it happened. I'd say at some later date, the bird told Siegfried about the leaf and the possible consequences. Siegfried should have kept the information to himself. But at some point, in an excess of misplaced trust, he confided about it to his wife. Unfortunately, she proved to be a serial blabbermouth and eventually passed the secret on to Hagen - with fatal results.

Wonder if you missed the scene in which Kriemhild told him. Yes, Kriemhild brought all this on herself by not keeping important secrets properly.