What user should own /usr/local/mysql on Mac?

Looks valid to me. This is what my mysql folder looks like:

drwxr-xr-x  17 root    wheel    578 May  7  2010 .drwxr-xr-x   8 root    wheel    272 Jun 11  2010 ..-rw-r--r--   1 root    wheel  17987 May  7  2010 COPYING-rw-r--r--   1 root    wheel   5139 May  7  2010 EXCEPTIONS-CLIENT-rw-r--r--   1 root    wheel   9339 May  7  2010 INSTALL-BINARY-rw-r--r--   1 root    wheel  62989 May  7  2010 READMEdrwxr-xr-x  46 root    wheel   1564 May  7  2010 bindrwxr-x---  15 _mysql  wheel    510 Jan 21 08:15 datadrwxr-xr-x   4 root    wheel    136 May  7  2010 docsdrwxr-xr-x  34 root    wheel   1156 May  7  2010 includedrwxr-xr-x  22 root    wheel    748 Jun  3  2010 libdrwxr-xr-x   4 root    wheel    136 May  7  2010 mandrwxr-xr-x  15 root    wheel    510 May  7  2010 mysql-testdrwxr-xr-x   3 root    wheel    102 May  7  2010 scriptsdrwxr-xr-x  35 root    wheel   1190 May  7  2010 sharedrwxr-xr-x  29 root    wheel    986 May  7  2010 sql-benchdrwxr-xr-x  16 root    wheel    544 May  7  2010 support-files

How did you install MySQL it if it didn't hook everything up correctly itself?

EDIT: and this is the general flavor of the data folder:

drwxr-x---  15 _mysql  wheel       510 Jan 24 08:15 .drwxr-xr-x  17 root    wheel       578 May  7  2010 ..-rw-rw----   1 _mysql  wheel    158773 Jan 24 08:16 $USER.local.err-rw-rw----   1 _mysql  wheel         4 Jan 24 08:15 $USER.local.piddrwx------   6 _mysql  wheel       204 Jun 16  2010 $SOME_DB_NAME1drwx------   6 _mysql  wheel       204 Jun  8  2010 $SOME_DB_NAME2drwx------  15 _mysql  wheel       510 Jan 18 11:23 $SOME_DB_NAME3drwx------  12 _mysql  wheel       408 Jan 20 14:40 $SOME_DB_NAME4-rw-rw----   1 _mysql  wheel   5242880 Jan 24 08:15 ib_logfile0-rw-rw----   1 _mysql  wheel   5242880 Jan 24 08:15 ib_logfile1-rw-rw----   1 _mysql  wheel  18874368 Jan 21 17:31 ibdata1drwx------  85 _mysql  wheel      2890 Jun  3  2010 $SOME_DB_NAME5drwx------  85 _mysql  wheel      2890 Jun  3  2010 $SOME_DB_NAME6drwxr-x---  71 _mysql  wheel      2414 Jun  3  2010 mysqldrwx------  21 _mysql  wheel       714 Aug 31 17:27 $SOME_DB_NAME7

I don't run Homebrew on my machine, so I don't know if this is of much help as far as that goes.

I had the exact same problem and MattDiPasquale’s answer worked for me. I had to keep running mysqld all the time to ensure MySQL was running properly. When I looked at MySQL in the System Preferences I realised I had the same error.