The database server suffered some corruption of its MyISAM tables. This was discovered and acted on by Pair. The only active involvement by tye, yitzhack and me was to decide that one particularly large table should not be restored. That table was for request statistics, so we've lost the access statistics per page, but that's a small price to pay.
I'm not sure what caused the table corruption. It became very manifest after I restarted the MySQL server, but maybe that was also what caused the corruption in the first place. Maybe it can be discovered earlier by frequently running show table status $table and/or check table $table.
As the recovery process employed by MySQL/myisamchk respectively repair $table seemed to be mostly rebuilding the MyISAM index from the raw table file, future decisions will likely weigh the recency of the last backup, as filling the database from a backup is much faster than rechecking/repopulating the table by scanning a MyISAM file.
Update: Added a crucial "maybe" in the first sentence of the second paragraph.