If virtual1 and micromat tech3's experiences are any indication, this seems quite normal. I know that most of the folks I've spoken to who have Apple Bluetooth keyboards report similar unreliability in trying to bring up the boot menu with it.
You may have misunderstood me: I too have seen comments and complaints about BT issues and Startup Manager beyond the ones you mention, so I know it's real. I'm simply saying that this clearly is not the kind of
BT keyboard behavior Apple intended, be it with the Option key or any other
Startup key combination, and as such I called it abnormal. Moreover, as measured by (the lack of relevant) Apple Discussions hits, the incidence of boot picker call failure is just too low to consider it 'normal' on that ground too. I suppose that's another way of saying that it doesn't look like a systemic issue with Apple's BT keyboards, despite comments blaming 'certain' keyboards to the contrary. But I also know that such appearances can be deceptive.
Be all that as it may, the interesting question is whether the problem can be resolved without (for instance) replacing the keyboard. I don't have a sure-fire solution, only some suggestions to try. In this context you mention that
... when the computer boots, the Bluetooth keyboard's power light blinks for a moment the same way it does when you press the power switch.
Contrary to what you think, I suspect this may in fact signify that your keyboard isn't properly paired; this includes the possibility that it is paired to more than one (local) Mac or iDevice. See the
Wireless Connection issue/Keyboard section of
Troubleshooting wireless mouse and keyboard issues for details. (This KB deals with Snow Leopard; there is a separate KB article for
Leopard. I haven't been able to locate specific articles for Lion or Mountain Lion, but I suspect they will follow the Snow Leopard guide linked to above.)
Should re-pairing of the BT keyboard etc. not lead to a resolution, it may help to realize that
RF interference doesn't have to be from other BT units to be disruptive. Likewise, there may be
USB interference. In addition, resetting
PRAM (despite the lack of obvious links to BT) and especially
SMC may restore full BT functionality according to a number of users. Finally, in case startup key problems persist, it may help to try Safe mode and (especially) Verbose mode to see if the keyboard is recognized during startup.
Who knows, one or the other suggestion might actually help...
