I have a new install of Mac OS X 10.8.1 and cannot get Adobe AIR to install. I previously could not get it to install under 10.8 either.
Logs that I've found are the following:
8/30/12 4:04:47.277 PM Adobe AIR Installer[6985]: Runtime Installer begin with version 3.4.0.2540 on Mac OS 10.8.1 x86
8/30/12 4:04:47.277 PM Adobe AIR Installer[6985]: Commandline is: -psn_0_10234306
8/30/12 4:04:47.278 PM Adobe AIR Installer[6985]: No installed runtime detected
8/30/12 4:04:50.900 PM Adobe AIR Installer[6985]: Relaunching with elevation
8/30/12 4:04:50.901 PM Adobe AIR Installer[6985]: Launching subprocess with commandline /Volumes/Adobe AIR/Adobe AIR Installer.app -ei
8/30/12 4:04:53.931 PM coreservicesd[34]: Application App:"Adobe AIR Installer" [ 0x0/0x9c29c2] @ 0x0x7fca6521a680 tried to be brought forward, but isn't in fPermittedFrontASNs ( ( ASN:0x0-0x9c49c4:) ), so denying.
8/30/12 4:04:53.932 PM WindowServer[90]: [cps/setfront] Failed setting the front application to Adobe AIR Installer, psn 0x0-0x9c29c2, securitySessionID=0x186a5, err=-13066
8/30/12 4:04:53.966 PM authexec[6990]: executing /Volumes/Adobe AIR/Adobe AIR Installer.app/Contents/MacOS/Adobe AIR Installer
8/30/12 4:04:54.158 PM Adobe AIR Installer[6990]: Runtime Installer begin with version 3.4.0.2540 on Mac OS 10.8.1 x86
8/30/12 4:04:54.158 PM Adobe AIR Installer[6990]: Commandline is: -ei
8/30/12 4:04:54.158 PM Adobe AIR Installer[6990]: No installed runtime detected
8/30/12 4:04:54.236 PM Adobe AIR Installer[6990]: Launching subprocess with commandline /bin/chmod -fRP +rw "/Users/Shared/Library/Application Support/Adobe"
8/30/12 4:04:54.239 PM Adobe AIR Installer[6990]: Launching subprocess with commandline /usr/sbin/chown -hfRP brosenberg "/Users/brosenberg/Library/Application Support/Adobe"
8/30/12 4:04:54.239 PM Adobe AIR Installer[6990]: Launching subprocess with commandline /bin/chmod -fRP +rw "/Users/brosenberg/Library/Application Support/Adobe"
8/30/12 4:04:54.242 PM Adobe AIR Installer[6990]: Launching subprocess with commandline /usr/sbin/chown -hfRP brosenberg "/Users/brosenberg/Library/Preferences/Macromedia/Flash Player/www.macromedia.com/bin"
8/30/12 4:04:54.245 PM Adobe AIR Installer[6990]: Starting silent runtime install. Installing runtime version 3.4.0.2540
8/30/12 4:04:55.746 PM Adobe AIR Installer[6990]: Cannot make symlink /var/folders/zz/zyxvpxvq6csfxvn_n0000000000000/T/FlashTmp.h7p3B3/temp/Versions/Current: Invalid argument
8/30/12 4:04:55.748 PM Adobe AIR Installer[6990]: Error occurred during copy operation; beginning rollback: [IOErrorEvent type="ioError" bubbles=false cancelable=false eventPhase=2 text="Error #2038" errorID=2038]
8/30/12 4:04:55.767 PM Adobe AIR Installer[6990]: Rollback complete
8/30/12 4:04:55.768 PM Adobe AIR Installer[6990]: Exiting due to error: [IOErrorEvent type="ioError" bubbles=false cancelable=false eventPhase=2 text="Error #2038" errorID=2038]
8/30/12 4:04:55.768 PM Adobe AIR Installer[6985]: Exiting due to error: [ErrorEvent type="error" bubbles=false cancelable=false eventPhase=2 text="Error #2038" errorID=2038]
8/30/12 4:04:55.770 PM Adobe AIR Installer[6990]: Runtime Installer end with exit code 7
8/30/12 4:04:58.966 PM Adobe AIR Installer[6985]: Runtime Installer end with exit code 7