Siegfried has his sword drawn during the fight in Gunther's hall. When Kriemhild's entry stops the fighting it hangs by his side again.
When Kriemhild wakes up finding her dead husband, Siegfried's chest visibly rises and falls, indicating breathing.
The tip of the spear Siegfied is killed with exits through the chest. Since Siegfried is invulnerable except at the entry point this should not be possible. The same impossible chest wound is shown later to be the one bleeding when the murderer enters the room.
How does Hagen know about Siegfried's vulnerable spot where the leaf fell (and even that it was a Linden leaf)? Siegfried himself seems unaware of it at the time, though he evidently later told Kriemhild who was able to mark the spot on his cloak with a cross (Hagen had asked her to do this so that he could 'protect' Siegfried). This anomaly appears to be present in the original poem. Some prints give the woodbird an extra verse beginning 'If by chance a leaf should fall', predicting the event before it happens, but Siegfried still appears to take no notice.
The leaf from the tree falls on a part of Siegfried's back already splashed with dragon blood. Therefore it should not leave a vulnerable spot.