When Joe is putting poison in champagne, some poison falls into his glass. Some of it can be seen on the glass in the next shot, but inside the liquid itself poison is absent.
When the pair kisses after Joe asks her to be his girlfriend, they are shown moving in for a kiss from a further distance than they were shown in previous shot.
At the first death in the movie, girl's nose bleed, but she was being strangled, so there should be no blood.
When the pair proposes to each other, you can see microphone in the glass (it's "hidden" behind Joe's head for most of the scene).
At the point when Kate says:"I was only doing it for you", we hear her say that, but her lips don't move.