When Peter goes to answer his iPhone, throughout the film you constantly hear two sounds when he answers it - the ringtone and the iPhone's "lock" sound. Normally, the iPhone only ever plays that sound when unlocking it. When you receive and answer a call, no sound is played other then the ringtone.
When Sydney is hit by the golf ball, the wound starts on his knee and is clearly shown, but later that day when he calls Pete about the Rush concert, the ice pack is now down near his foot, with no sign of the injury on his knee.
In the bar when Peter and Sydney are getting to know each other, they both down some whiskey, emptying their glasses. In the next shot, their conversation continues and both glasses still have whiskey in them.
In the boat race scene, Barry refers to himself and Peter as the "Anchors". However, they are the first in line to drink. In a boat race, the anchors would be the last two in line that have to drink two beers at one time.
When Peter is staring at Sydney's card in his office booth, about to call him for the first time, the hand holding the card is not Paul Rudd's (cf. close up to Peter's hand when he originally receives Sydney's card).