When my Flex Builder trial was coming to expiration and it was time to install my purchased license. Much to my chagrin, the Flex license manager (Eclipse > Help > Manage Flex Licenses) wouldn't accept my license with a confusing display: the checkbox was green indicating the serial was valid, but the message was "Serial number is invalid" and I could only close.
I contacted Adobe support via their web chat and was informed that this was a known technical bug, and I could either call tech support, or browse the User-to-User forums for the resolution. I haven't had good luck with those forums, but I figured it was worth a shot before searching the house for a phone. And I found the answer...
Sidenote re: chat customer service. Chat is available seemingly only when reps are available. A window will pop up and a button will appear on the page demonstrating a nice use of ajax. In my experience the reps are helpful, quick, and overly polite. I can just seem them with a list of phrases they only need to click to send like "Thank you for waiting", "Thank you for your patience", "Thank you while I read your issue". I suppose that's better than getting coffee or using the restroom while I wait (actual occurances).
Problem
Even when I'm logged into OS X as an administrator, Eclipse and/or the Flex Builder License Manager are unable to update the license settings file.
Solution
Close Eclipse or Flex and locate the license file to update it manually. On OS X it's at /Library/Application Support/Adobe/Flex/license.properties. The license key entry should have a line:
flexbuilder3=SerialNumberNoDashes
When you save it you'll likely be prompted for an admin password since this is a protected file. Fire up Eclipse/Flex Builder and you should be good to go. Confirm the license key is recognized by running back to the Help > Manage Flex Licenses... menu.
Footnote
I originally thought my serial wasn't being accepted because I had also installed this serial successfully on my laptop and was now installing on my desktop. Adobe indicates that installing on multiple machines is acceptable as long as you're not using both simultaneously, and customer support confirmed this use was not prohibited.
Additional Resources
Adobe Serial Number Issues
Adobe Customer Service
Adobe User-to-User Forums