noob: Calling linux GURUs, folder file permission for mysql data directory

[gold]

I can't start the mysql server. It complains about the file permission. I am pretty sure that I set the user=mysql to have access rwx to folder /home/me/mysql. Here is the error and folder permission:

071118 06:37:14 mysqld started
071118 6:37:14 [ERROR] /usr/libexec/mysqld: Can't create/write to file '/home/me/mysql/data/dev.pid' (Errcode: 13)
071118 6:37:14 [ERROR] Can't start server: can't create PID file: Permission denied
071118 06:37:14 mysqld ended

/home/me/mysql
drwxrwxr-x 3 mysql mysql 4096 Nov 17 18:08 .
drwx------ 30 me me 4096 Nov 18 21:17 ..
drwxr-xr-x 4 mysql mysql 4096 Nov 18 06:38 data

/home/me/mysql/data
[me@dev data]$ ls -la
total 20
drwxr-xr-x 4 mysql mysql 4096 Nov 18 06:38 .
drwxrwxr-x 3 mysql mysql 4096 Nov 17 18:08 ..
-rw-rw---- 1 mysql mysql 1320 Nov 18 06:37 dev.err
drwx------ 2 mysql root 4096 Nov 18 06:36 mysql
drwx------ 2 mysql root 4096 Nov 18 06:36 test

Can someone tell me why mysql server can't create the dev.pid file in /home/me/mysql/data?

[gold]

I gave user=mysql and group=mysql access to /home/me/mysql folder. Do I have to give access to user=mysql and group=mysql for intermediate folders like /home and /home/me? If so what permission, just executeable fine?

/home/me folder has this permission:
drwx------ 31 me me 4096 Nov 19 10:28 me

/home folder has his permission:
[root@dev me]# ls -la / | grep home
drwxr-xr-x 4 root root 4096 Aug 22 19:15 home

can I just make "me" folder executable for other only, like this, chmod 701 /home/me, would that help or I have to do chmod 711 /home/me, to cover the group?