I spoke a bit too soon about the upgrade being flawless. It turns out that one subsystem started failing after the upgrade, although it is not an out-of-the-box one.
I've included the description here in case someone runs into something similarly weird (especially with scripts calling MySQL?) and because although I have a work-around, I'm not sure (but can guess) as to the actual cause of the change.
This subsystem is on a pacemaker/corosync cluster, which as one resource group is running a resource agent (RA) for a bacula-fd instance. (The bacula-fd RA takes care of backing up those DRBD-mounted filesystems that are part of the resource group.) The bacula-fd was failing because as a run-before command on the backup job, it was executing the mysqlblasy.pl script to back up some MySQL databases. After the upgrade, mysqlblasy.pl started failing when running from bacula-fd, even though it could be run directly as root.
However, *none* of these components were upgraded during the 5.5->5.6 OS upgrade: mysql server & client mysqlblasy.pl bacula daemons/clients bacula RA pacemaker/corosync
After suitable diagnosis, I was able to determine that with CentOS 5.5, the environment provided to the RA had $HOME set, but that with CentOS 5.6 $HOME was *not* set. In particular, since this RA runs as root, in 5.5 HOME was set to "/" (as opposed to "/root"). Since there was no change to pacemaker, I suspect that there was either a change in the way daemons are started up, or a change to the fork or set[re]uid model (or something similar).
Ensuring that HOME was (re)set properly before invoking mysqlblasy.pl caused the backups to work again as expected.
Devin