Yes, it's true, a donated heart was dropped before it was transplanted into a patient in Mexico.
See video of the heart dropping incident
As a transplant professional I feel the need to weigh in on this. Yes, it is horrifying to watch something as precious as a donated human organ tumble to the ground. No, it shouldn't have happened. However, it is something we work very hard to prevent, and when it can't be prevented, we work hard to make sure the organ isn't harmed by packaging every single organ as though it might be dropped, or in a car accident, or some other mishap might occur.
Organs are always packaged with no less than three sterile barriers, so that if anything happens, such as a container coming open, the organ remains sterile. It is also important to note that organs are frequently transported anywhere from a few miles to over a thousand miles, so they have a risk of being in a car accident just like the average driver does.
Those simple facts mean that once in a great while the unthinkable does happen and organs have minor accidents. The good news is that an organ is far better packaged than your average driver! A typical abdominal organ has three sterile barriers and one of those may be a hard container. These are then placed inside a biohazard plastic bag along with ice, then those are inside a styrofoam insert which is placed inside another biohazard plastic bag inside a box with a 50 pound burst strength. All to protect the precious cargo inside against any kind of unexpected accident.
For thoracic organs, a cooler may be used instead of the box lined with biohazard bags, but the packaging is essentially the same.
This packaging is made mandatory by UNOS, the United Network For Organ Sharing. End result? The box, and the organ inside, can tolerate far more stress than you might expect. Keep in mind that organs have no blood in them when they are being transported, so they don't bruise, and any harm that might come to them is limited.
The recipient is reportedly doing well following heart transplant surgery.

