When he immediately turned into an intruder and hung out. Hung out in a way that if the lady simply turned her head she would she him.
The other problem was the tunnel that just happened to be connecting the two houses.
For me it's the fact that he lets a stranger make a call in his house while he is alone. I would never do that. And then he pushes it further by leaving him all alone in the room! I can buy that he's a nice guy and would let a stranger in for an urgent call, but leaving him all alone in a room is just stupid and unrealistic.
Also the whole second half at the lady's house was too surreal to be true, it's almost impossible she would never hear him make sounds on the floor, or would never feel his presence. But I think that part was intended to be ironic with hints of black humor. The party scene was subtly funny.
Overall I liked the movie but it's not to be taken as too realistic I think... that's what makes it good.