What features of the court made it undemocratic?

The main feature is that the Justices are not elected by the people.

Explanation:

The US Supreme Court Justices are not elected democratically by the people but they are instead nominated by the President and then after their nomination confirmed the the US Senate. Furthermore, they are serving indefinitely as long as they uphold the good behavior and can cast down laws passed as unconstitutional by the officially elected representatives.