Ben is running through the rain to the hospital, he arrives inside with his body 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 and he is soaked, but his shirt is completely dry.
The 911 operator gives the hotel address as 9212 West 3rd Street in Los Angeles. That address is in the middle of Beverly Hills not that far from Rodeo Drive. A seedy motel would hardly be situated there.
When the saltwater box jellyfish is placed into the bathtub, the water in the tub is freshwater and very cold. In a situation like that a jellyfish would most likely instantly roll up into a ball and die very quickly, rather than swim around and sting people.
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.
In her print shop, Emily prints a card on her letterpress to show Ben. Without inking her press, she produces a three-color piece in one pass. In reality, each color would require a separate pass, the press would need to be inked up before each pass, and cleaned after.
When Emily is having her heart transplant, her new heart starts beating for the first time. At this point, she would have to be on bypass (that is, connected to the pump-oxygenator, or "heart-lung machine") and yet we hear the sound of her being mechanically ventilated - this would not happen until she was ready to come off bypass.
Jellyfish can live in captivity as long as the tank they are in is round. Round tanks keep the jellyfish from getting trapped in the edges (from which they can't escape without a water current). In the movie, the tank that Will Smith's character uses for the jellyfish is round, so there is no error.
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.
Because eyes are not connected to the blood stream, eye donors do not need to be matched as closely as other organ donors. Because of this, it is doubtful that Ezra would be waiting for eyes. Also, in general eye donation does not cure blindness. Eye donors give only corneas, whole eye transplantation is not common yet. People who are born blind or have blindness due to a problem with the inner eyes (which causes most blindness) cannot be cured by cornea donations. Cornea donation is sort of like replacing a windshield. It's a simple and non-dramatic process.
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.
The goof items below may give away important plot points.
When Ben is in the bathtub with the jellyfish near the end of the movie, the amount of ice in the tub changes several times between different angles/shoots. Some times there are lots of ice, other times a bit of ice and other times no ice at all.
Will Smith is incorrectly listed in the credits as Ben Thomas. He plays the character Tim Thomas who in the course of the movie impersonates his brother Ben Thomas. Michael Ealy is credited as Ben's brother, when he in fact plays Ben Thomas.
After Ben donates a kidney to the hockey coach, he is out and about the following day. In reality, with modern minimally invasive kidney donor surgery, donors are up and walking the day of the surgery, and often discharged from the hospital after only 1 or 2 days.
Ben can hardly walk the same day that the bone marrow transplant, yet he doesn't have a limp later that day. You can see a slight limp when he walks up the stairs to meet Emily. She says she had company the last few of days, so it could be more than one day since the donation.