I would like to make a ruling like the following.
Scent:
Yes, if an invisible person is not moving and trying to be extremely silent, no check is needed, he is invisible. Only his scent may give him away to beasts and animals. So in that case, I prefer to have the PC succeed a stealth check vs. the passive perception of a beast within 60 ft.
Sound:
If the invisible character is moving, he makes noise. First, his feet may make sound on the ground. A soft and thick carpet? No sound. Crunchy leaves in a forest? Yeah he is making some noise. A stealth check is required. Walking on a rope bridge? Haha, he is definitely not that invisible.
His armor may create noise. If he is wearing metal armor, he needs a successful stealth check to remain undetected.
Tracks:
Generally if an invisible person is leaving obvious tracks behind him, he can be easily detected. Walking on a sand dune or a dusty/wet floor, a muddy ground, for instance. Otherwise, creatures with extremely sharp visual senses may spot the invisible character by subtle tracks left behind.