McMacker4

As i've seen in the screensot you uploaded, the one that said something about the architecture if your computer, that could mean many things. It could mean that this launcher can only run if it is in your Applications folder (which I doubt). Could mean that you are using the new launcher (which I don't think it supports PowerPC based Macs) thinking that you are using the old one...
Could be many things.

I' sorry to tell you but the older launcher will only let you play minecraft 1.5.2. but won't let you play 1.6.2 (the newest version) since the new launcher uses a different location on your hard drive to save the game's files. I'm afraid there is nothing to do but get a new computer. I'm sorry 😞

I don't think you can update java to 1.6 since you are using a PowerPC processor. You can't update to Mac OS X 10.6 Snow Leopard because this version of Macintosh is Intel only. I'm sorry I don't think there is anything to do in your case, just get a new Mac.

Well it's not a problem for me becase I have 10.8 already. But many other people will care about this...

Nice work Mojang. Well done. Keep it like this. 🙂

Yes, minecraft works on 10.6. I've personally tried it: it works perfectly.

Actually, they have already officially released 1.6.1. It was released on Monday, July 1.

I know that, Tails, but I want to be informed and if I didn't have mails activated I wouldn't ever know if this was solved or not...
But thanks anyways 🙂

OMFG Everyone seems retarded. Can't you see that it's not mojang's problem??? Its LWJGL's problem. Mojang can do NOTHING about this, just hope that they fix it. They perfectly know. Stop bothering Mojang, stop writing here about what should Mojang do or not and start writing on the LWJGL's forums about this. The only thing you are doing is spamming my mail and other people's mail, nothing else.
So, please, stop writing and wait patiently.

If you mean 13w17a I already tried it but it's still the same:

Launcher 0.6 (Dev) (through bootstrap 2) started on osx...
System.getProperty('os.name') == 'Mac OS X'
System.getProperty('os.version') == '10.5.8'
System.getProperty('os.arch') == 'x86_64'
System.getProperty('java.version') == '1.6.0_26'
System.getProperty('java.vendor') == 'Apple Inc.'
Trying to log in...
Logged in successfully
Getting syncinfo for selected version
Queueing library & version downloads
Download job 'Version & Libraries' started (8 threads, 1 files)
Delta time to compare resources: 13129 ms 
Download job 'Resources' skipped as there are no files to download
Job 'Resources' finished successfully
Finished downloading /Users/mcmacker4/Library/Application Support/minecraft/versions/13w17a/13w17a.jar for job 'Version & Libraries': Used own copy as it matched etag
Job 'Version & Libraries' finished successfully
Launching game
Launching!
/Users/mcmacker4/Library/Application Support/minecraft
Running: /System/Library/Java/JavaVirtualMachines/1.6.0.jdk/Contents/Home/bin/java -Xdock:icon=assets/icons/icon_32x32.png -Xdock:name=Minecraft -Xmx1G "-Djava.library.path=/Users/mcmacker4/Library/Application Support/minecraft/versions/13w17a/13w17a-natives" -cp "/Users/mcmacker4/Library/Application Support/minecraft/libraries/net/sf/jopt-simple/jopt-simple/4.4/jopt-simple-4.4.jar:/Users/mcmacker4/Library/Application Support/minecraft/libraries/com/paulscode/codecjorbis/20101023/codecjorbis-20101023.jar:/Users/mcmacker4/Library/Application Support/minecraft/libraries/com/paulscode/codecwav/20101023/codecwav-20101023.jar:/Users/mcmacker4/Library/Application Support/minecraft/libraries/com/paulscode/libraryjavasound/20101123/libraryjavasound-20101123.jar:/Users/mcmacker4/Library/Application Support/minecraft/libraries/com/paulscode/librarylwjglopenal/20100824/librarylwjglopenal-20100824.jar:/Users/mcmacker4/Library/Application Support/minecraft/libraries/com/paulscode/soundsystem/20120107/soundsystem-20120107.jar:/Users/mcmacker4/Library/Application Support/minecraft/libraries/org/lwjgl/lwjgl/lwjgl/2.9.0/lwjgl-2.9.0.jar:/Users/mcmacker4/Library/Application Support/minecraft/libraries/org/lwjgl/lwjgl/lwjgl_util/2.9.0/lwjgl_util-2.9.0.jar:/Users/mcmacker4/Library/Application Support/minecraft/libraries/argo/argo/2.25_fixed/argo-2.25_fixed.jar:/Users/mcmacker4/Library/Application Support/minecraft/libraries/org/bouncycastle/bcprov-jdk15on/1.47/bcprov-jdk15on-1.47.jar:/Users/mcmacker4/Library/Application Support/minecraft/libraries/com/google/guava/guava/14.0/guava-14.0.jar:/Users/mcmacker4/Library/Application Support/minecraft/libraries/org/apache/commons/commons-lang3/3.1/commons-lang3-3.1.jar:/Users/mcmacker4/Library/Application Support/minecraft/libraries/commons-io/commons-io/2.4/commons-io-2.4.jar:/Users/mcmacker4/Library/Application Support/minecraft/libraries/net/java/jinput/jinput/2.0.5/jinput-2.0.5.jar:/Users/mcmacker4/Library/Application Support/minecraft/libraries/net/java/jutils/jutils/1.0.0/jutils-1.0.0.jar:/Users/mcmacker4/Library/Application Support/minecraft/versions/13w17a/13w17a.jar" net.minecraft.client.main.Main --username mcmacker4 --session -7291198332017171864 --workDir "/Users/mcmacker4/Library/Application Support/minecraft"
---- YOU CAN CLOSE THIS LAUNCHER IF THE GAME STARTED OK ----
---- YOU CAN CLOSE THIS LAUNCHER IF THE GAME STARTED OK ----
---- YOU CAN CLOSE THIS LAUNCHER IF THE GAME STARTED OK ----
---- (We'll do this automatically later ;D) ----
Client> 249 recipes
Client> 27 achievements
Client> 2013-04-26 17:47:40 [CLIENT] [INFO] Setting user: mcmacker4
Client> 2013-04-26 17:47:40 [CLIENT] [INFO] (Session ID is -7291198332017171864)
Client> Invalid memory access of location 0x0 rip=0x0
Client> 
Game ended with bad state (exit code 139)

Ok, everyone says it's fixed but not for me, I still get these spaces between textures and it's EXTREMELY annoying. I'm using 1.5 official release...

You should read about Silk Touch Enchantment on minecraftwiki.net, this will solve your problem...
u_u