pt-table-checksum and row-based replication
I do not understand why an application requires the MIXED replication format, as MIXED is equal to STATEMENT-based, but changing to ROW format when executing "unsafe" queries. So, a MIXED-compatible application should be compatible with both STATEMENT and ROW.

As you can see here, if the the format detected (server-side) is ROW or MIXED, it tries to change it dynamically for the session only. In your case, it complains about one of the slaves here (it requires SUPER privileges).

Assuming you do not have a 3-node chain replication, or you use the slave's binlog for anything, you can ignore the warning with --no-check-binlog-format. No need to change the my.cnf. The question is, will the session-only change to statement affect your "application that requires MIXED"? pt-table-checksum requires its own calculations to be done as statements, as a hash has to be calculated independently on the master and the slave independently and synchronously (not in time, but in relation with other queries).