Do SSD drives need Check Disk?
Yes. All drives have the potential for file system corruption, due to corruption by the drive - (very rare on SSDs, but can still happen), power failure, system crash, etc.
What is more important, rather than drive technology, is the format used. Formats like FAT32 are unstable, and system crashes, power failures, etc. can severely corrupt the files and directories on the drive. You may need to use checkdisk software in order to repair the corruption.
Modern formats like NTFS are very stable, and highly resistant to system crashes and power failures. However, SSDs with a write-back cache but without a supercapacitor backup, can still allow NTFS partitions to be corrupted in a power failure situation. [SSDs without write-caching (e.g. Intel) or a write-cache with backup supercapacitor (e.g. Sandforce controller), are safe].
There is no need to regularly perform a surface scan, with SSDs - as the internal processor will periodically move data around as part of 'wear levelling'. When it is moved, it is checked for accuracy, and defective parts of the flash memory are deactivated and the data moved to a spare area.
That said, there is no need to perform surface scans of conventional HDs. The internal processor in normal HDs will regularly scan the data when idle, to ensure that all the data is readable, and weakening areas of data will be 'repaired' by moving the data to a spare area automatically.
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Summary. SSDs are no different to HDs in terms of getting errors.
Most errors are software errors, caused by saving to the drive being interrupted by a serious system crash or power failure. Checkdisk will be required to check that the files are OK under some circumstances (very few on NTFS or other advanced formats).
Normal HDs can be protected from corruption by system crash and power-failure by disabling 'write caching' - but this is very slow. Some SSDs have ways of getting around this.
Errors on the drive (bad sectors) can occur on SSDs and HD (but are rare on SSDs). Both types of drive technology regularly scan the data automatically to check for bad sectors.