Can something go wrong by having a blood transfusion?

Yes, many things, blood transfusions can cause death if they give the wrong type, as of wrong blood group or of Rh positive to negative.

Also it is possible to be exposed to a bloodying pathogen such as HIV or hepatitis. Modern testing greatly reduces this risk, but there still remains a small risk. Blood typing/matching errors are extremely rare. There is always a risk (albeit small) any time you receive tissue into your body from another person whether it is blood, an organ, bone, skin, etc.

============= FROM THOMAS, --You might consider carefully the latest change of the use of Non-Blood-Surgery, medicine & therapy by the Dept. of Defense ( military): On the "Clinical Posters" web site this is stated by the Military: "U.S. Military Training for Bloodless Surgery" "Non-blood Medical management, once considered a fanatical patient view of Jehovah's Witnesses is now becoming the gold standard for surgery" (Answers.com does not permit web addresses for reference) ---

ALSO THE COMMITMENT by the Military with the Elmwood , New Jersey Hospital by the grant of some 4.6 million dollars with the Hospital for training & use of technology with their medical staff ! Their ground breaking activity has been in use for 15 yrs.