How to handle OS X firmware updates that won't install
If you've got an OS X firmware update that just refuses to install properly, there are a few things you can try to remedy the situation.
When Apple releases Mac firmware updates, the system undergoes a special installation procedure in which it shows a progress bar on a gray screen and then reboots. If you have an update available but do not see the progress bar when applying it, it may not have installed properly. As such, you may see the update still showing in Apple's Software Update service.
There are some special requirements for handling firmware updates as opposed to standard software updates, and if they are not met, the system may fail to install the update.
The first requirement is to ensure that your operating system version is fully updated, so if you see any system updates in addition to the firmware update available, install those first.
The second requirement is that the system needs to be connected to a reliable power source to install firmware updates. If you have a laptop system, be sure that the AC adapter plugged in and that the charge light is on. If the charge light is blinking amber or is red, that indicates a problem with the power adapter or charging circuits in the system; you may need to have these items serviced or replaced before the update will install.
In addition to checking the power, try resetting the Mac's System Management Controller (SMC), as this controller unit is responsible for how power is handled in the system. Errors with the SMC may also be responsible for any blinking amber warning lights in the attached AC adapter.
If the update still does not install, next try checking your boot drive for errors. To do this, reboot to the recovery drive by holding Command-R, and then open Disk Utility from the OS X Tools interface. In here, use Disk Utility to verify the boot volume (i.e., "Macintosh HD") for formatting errors, and also choose the drive device and rerun the verification to check for partitioning errors. Fix any errors that show up. Along with these drive checks, use Disk Utility to run a permissions fix on the boot drive.
After following these steps, try rebooting again to see if the issue has been resolved. If not, remove any residual traces of past update attempts by opening the System > Library > CoreServices > Firmware Updates directory and moving any items in this folder to the desktop. Then try downloading the relevant updater manually from the Apple Support Downloads page and run it. You can search for the update on this page or, for more recent updates, you'll see them listed at the top of the page.
As a last resort, you can try installing the firmware update from a fresh OS installation. Attach an external hard drive and reboot the system with Command-R held down to load the recovery drive. Then install a fresh copy of OS X to the drive. This will ensure a factory-default software environment in which you can try applying the firmware update. After the firmware update is installed, you can open the Startup Disk system preferences and select your main boot drive again.