MySQL slow query log logging all queries

It sounds like log_queries_not_using_indexes is enabled.

Check it by doing:

mysql> show global variables like 'log_queries%';
+-------------------------------+-------+
| Variable_name                 | Value |
+-------------------------------+-------+
| log_queries_not_using_indexes | ON    |
+-------------------------------+-------+

Turn it off with:

mysql> set global log_queries_not_using_indexes = 'off';
Query OK, 0 rows affected (0.00 sec)