There are various ways in which modern hard disks handle errors.

Most hard disks use ECC`s error correcting codes mostly the Reed-Solomon error correction techniques.
The error checking codes usually employ the use of complex algorithms mathematically derived to store extra bits. These bits are used to correct various errors.
Nowadays most of the drives support LDPC or the low density parity check codes.
The LDPC allows performance to reach the Shannon limit and also result in the highest storage capacity drives.   _{Your Comment}