I get a "serious errors while checking the disk drives for /boot" error while booting

The message says some errors were found on the filesystem which fsck is afraid to fix automatically, so you need to do it manually. To do this, press M when it prompts you - this will drop you into a emergency root console. From there you'll be able to run

fsck /dev/sda1

where /dev/sda1 is the name of your /boot partition. You can see the list of partitions by doing fdisk -l.

Alternatively, you can try fsck -A to check all partitions but I suppose it'll only work if the root partition is already mounted so fsck can access /etc/fstab.

It'll probably ask you a few questions - I usually just agree with what it proposes. Also, there's 'a' option which will fix things automatically but the man file suggests to use it with caution. So, ultimately, fsck -Aa should fix all errors on all partitions without asking any questions.

After you're finished, exit the shell with Ctrl-D and the machine will reboot.

I had a similar problem except I had created a RAID volume formatted with XFS. Every time the OS booted I would get the Serious errors were found... message. If I hit i to ignore, the volume would still mount fine.

All I had to do was install the xfsprogs package and run xfs_check. The OS was probably trying to check the filesystem but failed because the utility wasn't there.

Thanks for steering me in the right direction Sergey!