When Emily's new heart starts beating for the first time, she would have to be on bypass, connected to a pump-oxygenator ("heart-lung machine"). The scene includes the sound of her being mechanically ventilated, which would not happen until she was ready to come off bypass.
Ben runs through the rain to the hospital. When he arrives inside his body is soaking wet, but his shirt is dry. When he walks out of the hospital, it still is pouring rain and his shirt becomes visibly soaked. When he arrives at his motel, he opens the door soaked, but his shirt is completely dry.
When Emily demonstrates the manually-fed treadle printing press with a blank sheet of paper from the pile, the printed piece is in full color. This press is single-color and can only print one color at a time.
At the beginning of the movie, Ben incorrectly states that God created the world in 7 days, but in fact the Bible says it was created in 6 not 7; 5 for creating the universe, 1 for creating man, and rested no the 7th.
Ben puts his car in "park", but it rolls a few feet before stopping. That is normal for a car with an automatic transmission; put into "park," it will roll a little to take up slack in the transmission.
It's very unlikely that Ezra would wait for an eye transplant. Eyes are not connected to the blood stream, so eye donors don't need to be matched as closely as other organ donors. Eye donors give only corneas; whole eye transplantation is not common yet. Cornea donation is sort of like replacing a windshield. People who are born blind or have blindness due to an inner-eye problem (which causes most blindness) cannot be cured by cornea donations.
When Ben and Emily are driving in his car with the dog in the back, the back window is open and the dog puts his head out of the window, but its mouth does not move. If they were really driving, the dog's mouth would move because of the wind.
Box jellyfish poison causes elevated potassium levels in the victim's blood, leading to cardiovascular collapse and death in as little as two to five minutes. By itself, that would not make the victim's organs unsuitable for transplant.
After Ben donates a kidney to the hockey coach, he is out and about the following day. With modern minimally invasive kidney donor surgery, donors are up and walking the day of the surgery. They're often discharged from the hospital after 1 or 2 days.
Ben can hardly walk the same day as the bone marrow transplant, yet he doesn't have a limp later that day. He has a slight limp when he walks up the stairs to meet Emily. She says she had company the last few days, so it could be more than one day since the donation.