According to the lesson, the biggest risk of organ transplantation is

Hello.  I am happy to help you out.  There are a few risks for patients that have undergone an organ transplant.

1)  There is a risk of rejection of the transplanted organ.
2)  There is also an increased risk of infection due to the immunosuppressant medications.
3)  Any of the side effects of the immunosuppressant medications as previously discussed.
4)  It is important to note that there is a very small risk for acquiring AIDS, Hepatitis B, other viruses, or cancer from the donor organ.  Organ donors are screened very carefully for these diseases; however, on very rare occasion, they are undetectable and may be passed to the recipient.
5)  There is a potential for a blood transfusion due to blood loss in the operating room and related risk for the transmission of infectious diseases from a blood donor.  Blood donors are screened very carefully, but there may be a rare case when a disease may be undetectable and may be passed to the recipient.

Hope that helps!  :)  Biology rocks!