Went very smoothly.
The only things I had to be really careful about were a few manual customizations that were overwritten during upgrade. Viz.:
My /opt/zimbra/conf/salocal.cf.in has some custom scoring for additional RBLs. By keeping a copy of the original (pre-modification) file, I was able to confirm (using diff) that the upgrade didn't change anything in the default configuration, so I could just copy my custom file back into place. I also grep'ed the rbl addresses against /opt/zimbra/conf/spamassassin to make sure they hadn't been added to SA's default scoring during the upgrade. (If they had, I'd have adjusted or removed my custom scoring.)
My /opt/zimbra/conf/amavisd.conf.in had a customization to deal with Bug 45607 - Suspect.Bredozip-zippwd-13 .zip virus not detected, but I confirmed that modification is now standard in Zimbra. But after installing 6.0.7, I still had to modify the file to patch another bug, Bug 48405 - debug address left in amavisd.conf file. This will be gone in 6.0.8.
/opt/zimbra/conf/clamd.conf.in needed a small modification to deal with Bug 48824 - Amavis/SA: Heuristics.Phishing.Email.SpoofedDomain not detected on delivery (see comment 8). Hopefully this will be fixed soon.
Due to the fact that ZCS 6's installation and zmschedulebackup can't write zmbackup with the --noZip option into the zimbra crontab, some manual customization was needed here, too. I found it was easiest to just do zmschedulebackup -D and then edit the crontab to add --noZip to the lines for full and incremental backups. Hopefully Bug 45634 - add noZip option to zmschedulebackup will be addressed sometime in GnR.
Otherwise, no hiccups whatsoever.