One option that doesn't require any external drives or disks:
Disk Utility's repair disk is largely* a thin wrapper over the unix
fsck (stands for "File System Check") utility. You can run it by:
- Booting into "Single User Mode" by rebooting and holding command-S during startup.
- A command-line input will appear; enter
- Wait for it to complete. If you see
**** FILE SYSTEM WAS MODIFIED ***** then run it again, since sometimes fixing the first errors will uncover more.
- Repeat until it says that the disk appears to be ok.
Reboot to boot normally.
*I can't find any indication that Disk Utility's "Repair Disk" function does anything that fsck doesn't. Nonetheless, Apple recommends that you use Disk Utility instead when that is an option.