I am using Firewire 800 and have three drives daisy-chained (3 TB Seagate GoFlex, 4 TB Seagate GoFlex Backup Plus and a 4-bay Drobo). I recall posting something on this already, but the bottom line is this: you CANNOT ALLOW your external Seagate drive to sleep on its own - Mac OS X ML will correct the drive when I attempts to write to the drive just prior to shutdown - the drive takes too long to spin up and something goes wrong.
I noticed that when I manually unmounted the drives and disconnected the Firewire cable, before shutting down my Mac, I never had the problem. Failure to do this would, eventually, cause all of the problems folks are describing above (read-only mounting on reboot and inability to correct with Disk Utility). I doesn't matter if you wipe / re-partition and reformat.
So... all of my problems went away when I performed the following steps (I found these on a Seagate support forum):
1. Connect the drive (I use FW800)
2. Install the included Seagate Drive Settings software and make sure you reboot your computer afterward
(Software also available from Seagate with your drive)
3. Seagate does not make the next steps obvious, you have to search for them.
Confirm that your drive is connected directly and correctly.
The drive must be connected directly to the Mac's USB or Firewire port to ensure that the spin-down command is sent to the drive. Do not connect the drive to a USB or Firewire port on the computer monitor or on the keyboard.
Click on the Apple > Choose System Preferences.
Click on the Energy Saver Icon.
There is Check box that says Put the hard disk(s) to sleep when possible.
Check the box here to set the drive(s) to sleep after 10 min of inactivity.
(Removing the check mark will disable disk sleep.)
Check what the disk sleep settings are now (if desired).
Click on the Apple > About this Mac.
Open the System Profiler.
Click on More Info.
Click on Power in the left column. The current Disk Sleep time is displayed in minutes on the right.
4. Another absolutely critical step that Seagate does not tell you anywhere is that in order for the firmware update from the last step to actually take effect (regardless of what the System Profiler says), you must power the drive down (disconnect the power supply from the hard drive and wait 10+ seconds) and then plug it back in.
5. Erase the drive using Disk Utility and partition as desired (you may be able to get away without this but this is what I did and it worked)
6. Go back to System Preferences, select Time Machine, click Select Disk and choose your new Seagate drive.
Yikes! However, when I did the above steps, everything works and I can boot / reboot / whatever without corrupting my Seagate drives (I never had these issues with my Drobo) and I have since filled all of the Seagate drives with data - no issues and they checkout fine with Disk Utility.