At 16:07, it is shown that Nathan had been punctured in his right abdomen by a piece of wood. He subsequently dies from the injury. The fact is, there are no major organs where he was punctured and the only issue would be internal bleeding. In actuality, he would be able to survive the injury for several hours, even if he did not get medical care.
The Red Sox rally to beat the Yankees in a game that's over before 11:49 am on a Tuesday. No MLB game starts early enough for that result to be broadcast by then within the same time zone.
It had been established that Nathan can feel Audrey's touch.
In one of Audrey's do-over days she flicks Nathan's ear with her finger and he reacts with pain. But Nathan's trouble in Haven is that he can't feel anything, so he shouldn't have reacted at all.