Final answer:
Doctor Manette's calm demeanor and his critical nature of others are the details in the text revealing his good reputation with the tribunal; unkempt appearance and mental illness history are not typically associated with a good standing.
Step-by-step explanation:
The details in the text that reveal to the reader that Doctor Manette has a good reputation with members of the tribunal are c) His calm and composed demeanor and d) His harsh criticism of others.
These qualities are typically respected and can indicate a person of good standing in a community or professional circle.
In contrast, details such as a) unkempt appearance and b) history of mental illness are generally not associated with a good reputation, especially in the historical context of Doctor Manette's character.