After Eckhart's character falls onto the street, only one ambulance arrives to the scene. The people trying to revive him on the street are wearing white uniforms. But when it cuts to the scene inside the ambulance vehicle, the workers are wearing blue uniforms.
When Ember meets Cameron in his subconscious, a wound forms in his chest for no apparent reason. He drools blood from his mouth just before being eviscerated, and we see blood running down his chin and temple in another shot, despite the previous shot not showing him spitting it up. Aside from this theatrical cut scene change, the unrated cut shows him spitting up blood, which is how it gets on his face. This was most likely a re-edit done to ensure that the film received a PG-13 rating from the MPAA.
When Cameron looks at the phone in the bathroom, the phone shows it's 11:21 PM. A few seconds later, when he is in his bed, the alarm clock shows 10:44.
After the daemon/boy kills the father, all that happen was that two paramedics came and collected the body, no questions asked. In real, the place would have been swarming by police since his death hardly was by natural cause.