Did the incorrect blood transfusion my father received play a role in his death, and am I responsible for that because I did not object to it?

If the cause of death was a mismatch between the added blood type and the original, then this is an accidental killing (qatl khata') that necessitates repentance and seeking forgiveness. It also requires the payment of diyah (blood money) and kaffarah (expiation) from the responsible doctor or nurse. There is no legal responsibility on the son of the deceased, as determining the blood type is the responsibility of the supervising doctor. You have the right to sue the party responsible.

The imams have mentioned various opinions regarding the liability of a doctor: Imam Al-Shafi'i states that a doctor is liable if he performs an act that a person seeking to do good would not perform, and he was aware of it. Al-Khattabi sees a consensus that a healer is liable if he transgresses and the patient perishes. Ibn Uthaymeen believes that a doctor is liable if the death was due to his error or if he was unskilled, but he is not liable if he was skilled and no error occurred on his part. Ibn Jibreen holds that whoever administers medicine while not being knowledgeable and causes harm is liable.