The bug is a regression introduced in 5.1 by the patch for bug28404.

Under some circumstances test_if_skip_sort_order() could leave some
data structures in an inconsistent state so that some parts of code
could assume the selected execution strategy for GROUP BY/DISTINCT as
a loose index scan (e.g. JOIN_TAB::is_using_loose_index_scan()), while
the actual strategy chosen was an ordered index scan, which led to
wrong data being returned.

Fixed test_if_skip_sort_order() so that when changing the type for a
join table, select->quick is reset not only for EXPLAIN, but for the 
actual join execution as well, to not confuse code that depends on its
value to determine the chosen GROUP BY/DISTINCT strategy.


mysql-test/r/distinct.result:
  Added a test case for bug #34928.
mysql-test/t/distinct.test:
  Added a test case for bug #34928.
sql/sql_select.cc:
  When changing the table's join type to JT_NEXT in 
  test_if_skip_sort_order(), also reset select->quick because other
  code may depend on its value to determine the GROUP BY/DISTINCT
  execution strategy.