The quality of data stored in individual blocks of memory cells of a flash memory system is monitored by a scrub read of only a small portion of a block, performed after data are read from less than all of a block in response to a read command from a host or memory controller. The small portion is selected for the scrub read because of its greater vulnerability than other portions of the block to being disturbed as a result of the commanded partial block data read. This then determines, as the result of reading a small amount of data, whether at least some of the data in the block was disturbed by the command data read to a degree that makes it desirable to refresh the data of the block.