In 24:14 it says, "והנה אהרן וחור עמכם מי בעל דברים יגש אליהם" - Behold Aharon and Hur are with you. Whomever is part of a dispute should approach them.
Moshe was not going away for a long time. He was going for 40 days. Couldn't they just wait until he got back if they would need a beis din? They probably would have no need for it anyway, because "theyw ere all camped as one" - they were not fighting.. so whyw as it so important for Moshe to appoint Aharon and Hur as the people in charge?
A leader cannot leave things vague.
If Moshe was away and was needed, it would create chaos among the people. He had to be very careful to appoint replacements, even though his departure is only temporary and short-term. Even if just for appearance sake, so the people would know that they have not been abandoned.
A leader has to make sure the people are taken care of, and he has to make sure the people feel they are being taken care of.