Hello,
The other day at my friends house I tried to get the new launcher set up on their mac. For some reason Minecraft will not let Mac Mountain Lion users play 1.6
Related issues
duplicates
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One thing I remember is that it said Mac Mountain Lion 10.5.3 (I think, or maybe 10.5.8? Sorry, I am unfamiliar with Mac's)... Sorry that I cannot give more information, like I said it is my friend's computer. I will contact him for the exact error message and post it no later than next Thursday. Thanks

Minecraft 1.6 does not work in 10.5.8 due to bug in LWJGL.

Is this still a concern in the current Minecraft version? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.

Mountain Lion = 10.8.x
Lion = 10.7.x
Snow Leopard = 10.6.x
Leopard = 1.5.x
Without more information I can only say that this is not confirmed.
And I'm typing this from a mac with mountain lion installed.