I see in some places that I need to chmod certain directories 777 and others 0777. I don't really see a difference. Is there one?

Well since there is no 0777 I think not LOL typo no doubt.

777 is the highest you can set with that being all permissions for everyone. Come attack me !

I've seen it several times, and when I actually used that command:
chmod 0777 directory
there weren't any problems. Go figure.

Actually chmod does technically have 4 digits.
I think if you leave any digits off, it's presumed to be a zero.

From: http://www.ss64.com/bash/chmod.html

The first digit is the user who owns it. (u)
The second is other users in the file's group (g)
The third is other users not in the file's group (o)
The fourth is All Users (a)

The hidden digit

Hi,
If you give chmod only three digits, then the highest bit is assumed to be zero. So, "chmod 077"=="chmod 777".
That highest bit means:
4=setUID
2=setGID
1=sticky
If you don't know what those mean, don't screw around with them.