ORA-24005 and ORA-24002 on table DROP

If table drop ends with message

ORA-24005: Inappropriate utilities used to perform DDL on AQ table [queue_table_name]

first try drop through package DBMS_AQADM with force=true

BEGIN
  SYS.DBMS_AQADM.drop_QUEUE_TABLE(QUEUE_TABLE =>'[queue_table_name]', FORCE=> TRUE);
END;
/ 

But what to do if it returns

ORA-24002: QUEUE_TABLE [queue_table_name] does not exist
ORA-06512: at "SYS.DBMS_AQADM", line 240
ORA-06512: at line 2

Your data dictionary is already little bit corrupted. You can try following

alter session set events '10851 trace name context forever, level 2';
drop table [queue_table_name];