Master/Slave desyncronisation
Assuming you have corrected the slave drift, you can just "start slave" again, but


You may need to skip some transactions, if they have been manually applied to the slave- you can do that with SET GLOBAL sql_slave_skip_counter
You probably have other differences between the master and the slave, because of the operations you mentioned or because of the skipping of transactions. In that case, using pt-table-checksum and pt-table-sync can help you resync the slave without having to reload the full contents.