At one point Helen chastises Anna for asking her "more questions than Jeopardy". Jeopardy! is an American quiz show that has only been briefly aired on British television. Even though it is well known in the UK, it isn't sufficiently part of popular culture that two British women would use this show as an analogy.
When James and Helen are sitting in the diner, they are drinking pink milkshakes. As the shots cut back and forth the shakes disappear and reappear. Also in the next scene James talks about drinking chocolate shakes, even though they were pink, not brown.
After having her cut treated at the hospital, Helen returns to the flat. She finds Gerry is not yet dressed and asks if he has only just gotten up, adding that it is 4 o'clock in the afternoon.
Earlier she went to work and was immediately fired, attacked whilst hailing a taxi and taken to hospital, after which she went home. Even allowing some time for travel, it is still unlikely that she was at the hospital for 6 hours.
The goof items below may give away important plot points.
At the end of the film when Helen and James are on the bridge, her hair is wet when James is explaining his situation. Then when she is crossing the street to use the phone, its still raining but Helen's hair is completely dry.