An apparent issue in the versions of OS X that are preinstalled on Macs shipping from the factory is causing headaches for some users, where they may run into problems if they try to reinstall OS X or restore from a backup.
As described by MacNN and MacTrast, the issue appears to happen because of a permissions problem that results in a compatibility error when the Mountain Lion installer is downloaded and run on an affected computer. Instead of installing as it should, users see a warning that states the current system is not compatible with Mountain Lion, with the only option to click "OK" and cancel the installation. Apparently affected systems may also have difficulty restoring from Time Machine backups as well, where they may see an error stating that the system could not add a recovery system to the destination disk.
While this issue seems to be a problem for users, for some this behavior may simply be a matter of compatibility with the Mountain Lion installer that is available on the App Store. The OS X installer includes a list of compatible systems on which it can be installed, so if the installer you are accessing is older than the system you are currently using, it will not have the machine code for your system and will therefore issue an error when you try to download and install the OS from the App Store program itself (including manually created Mountain Lion installation DVDs).
This may happen for new systems that ship with OS X Mountain Lion, which may seem odd since they are already running the OS and therefore ought to reinstall just fine. However, for any new system that shipped with Mountain Lion, if you want to reinstall the OS, do not go through the App Store; instead use the OS X recovery partition to access the appropriate installer for it.
Unfortunately, according to MacNN and MacTrast, this issue also applies to the OS X recovery partition, so even using the tools that download machine-compatible versions of the OS X installer are not able to install.
Luckily for those experiencing this problem, there may be a workaround in repairing the installation volume's permissions using Disk Utility before reinstalling OS X. In its description of the workaround, MacTrast mentions to repair the install drive, which means to run a standard permissions fix on the system's internal boot drive. While one might infer this to mean Recover HD partition itself, keep in mind the recovery partition is a mounted volume stored in a read-only disk image that cannot be modified. Additionally, the OS X permissions database does not extend to items on this volume, so there are no instructions available for adjusting its permissions. Therefore, if you try a permissions repair as a fix, you will only be able to do so for the boot drive.
Additionally, since this appears to be a permissions-related problem on the internal boot drive, an alternative approach that should work is to bypass the internal boot volume completely by restarting with the Command-Option-R keys held down to force the system to load the Internet Recovery tools (they will download when the spinning globe icon appears). Then use the Disk Utility version in these tools to first partition and format the drive, and then install a fresh copy of OS X to it.
If you are still running into errors, try attaching a secondary USB or FireWire hard drive to the system and then boot to the recovery tools and install OS X to this drive after partitioning and formatting it. Then boot to this drive (you can select it by holding the Option key at startup or choosing it as the default startup volume in the , format the internal drive, and repeat the installation process to reinstall OS X to the internal drive.
Be sure before you perform any of these reinstallation steps that you have a full backup of your system using Time Machine.