Jamieson, Fausset and Brown on Numbers 20:29

29. When all the congregation saw that Aaron was dead--Moses and Eleazar were the sole witnesses of his departure (Nu 20:28). According to the established law, the new high priest could not have been present at the funeral of his father without contracting ceremonial defilement (Le 21:11). But that law was dispensed with in the extraordinary circumstances. The people learned the event not only from the recital of the two witnesses, but from their visible signs of grief and change; and this event betokened the imperfection of the Levitical priesthood (He 7:12).

they mourned for Aaron thirty days--the usual period of public and solemn mourning. (See on De 34:8).