As of the time of this post, both the 1.24b TFT and RoC Mac standalone patch linked below have been stripped of their resource forks, compressed and uploaded to the server. As the files have no resource fork when uncompressed, they cannot be run in OS X. The extracted files appear as a grey rectangle with green "exec" text shown - it should appear as a black bnet icon.
http://ftp.blizzard.com/pub/war3/patches/mac/War3ROC_124b_English.zip (RoC)
http://ftp.blizzard.com/pub/war3x/patches/mac/War3TFT_124b_English.zip (TFT)

Until this is addressed by Blizzard, your best bet is to grab the 1.24a patch and then connect to battle.net to automatically download the 1.24b update.
http://ftp.blizzard.com/pub/war3/patches/mac/War3ROC_124a_English.zip (RoC)
http://ftp.blizzard.com/pub/war3x/patches/mac/War3TFT_124a_English.zip (TFT)

Thank you, I_mass_ents. I'll make sure that those who need to know are informed.

By the way, this should be fixed now.

I think this is what Maged is referring to.

To install a patch manually:

For players using StarCraft installed using the original CD set, use the following patch instructions:

1) Find the Starcraft folder on your hard drive, and open it.
2) Drag all the files from inside the "Brood War v1.16 OSX" folder into the Starcraft folder.
3) Transfer any maps you wish to keep from the "Maps" folder found in the Starcraft folder to the "RENAME ME Maps" folder.
4) Delete your "Maps" folder from the Starcraft folder.
5) Rename your "RENAME ME Maps" folder to "Maps" (minus the quotes).
6) Select the Starcraft file in your Starcraft folder.
7) Choose Make Alias from the File Menu.
8) Move the new alias file to the Desktop or Dock
9) Double click the Starcraft alias to play.


For players using StarCraft installed using the 1.15.2 digital installer, use these patch instructions:

1) Find the Starcraft folder on your hard drive, and open it.
2) Drag all the files from inside the "Brood War v1.16.1 OSX" folder into the Starcraft folder.
3) Transfer any maps you wish to keep from the "Maps" folder found in the Starcraft folder to the "RENAME ME Maps" folder.
4) Delete your "Maps" folder.
5) Rename your "RENAME ME Maps" folder to "Maps" (minus the quotes).
6) Double click the Starcraft (Carbon) application to play.

I found this out about 15 minutes ago, and I've reported it up my chain of command to get it fixed.

Thanks, guys!