ORA-30926: unable to get a stable set of rows in the source tables

This is usually caused by duplicates in the query specified in USING clause. This probably means that TABLE_A is a parent table and the same ROWID is returned several times.

You could quickly solve the problem by using a DISTINCT in your query (in fact, if 'Y' is a constant value you don't even need to put it in the query).

Assuming your query is correct (don't know your tables) you could do something like this:

  MERGE INTO table_1 a
      USING 
      (SELECT distinct ta.ROWID row_id
              FROM table_1 a ,table_2 b ,table_3 c
              WHERE a.mbr = c.mbr
              AND b.head = c.head
              AND b.type_of_action <> '6') src
              ON ( a.ROWID = src.row_id )
  WHEN MATCHED THEN UPDATE SET in_correct = 'Y';

A further clarification to the use of DISTINCT to resolve error ORA-30926 in the general case:

You need to ensure that the set of data specified by the USING() clause has no duplicate values of the join columns, i.e. the columns in the ON() clause.

In OP's example where the USING clause only selects a key, it was sufficient to add DISTINCT to the USING clause. However, in the general case the USING clause may select a combination of key columns to match on and attribute columns to be used in the UPDATE ... SET clause. Therefore in the general case, adding DISTINCT to the USING clause will still allow different update rows for the same keys, in which case you will still get the ORA-30926 error.

This is an elaboration of DCookie's answer and point 3.1 in Tagar's answer, which from my experience may not be immediately obvious.

You're probably trying to to update the same row of the target table multiple times. I just encountered the very same problem in a merge statement I developed. Make sure your update does not touch the same record more than once in the execution of the merge.