Collation conversion latin1 -> utf8

[ccarmical]

<BACKGROUND>
I have successfully upgraded to the 4.1 series with no major problems. The only thing that is a little inconvenient is the inability to use phpMyAdmin to administer the database. The problem, apparently, is that my database was originally set up as latin1, even though I am actually using utf8.

Because of this, I cannot view the data from within phpMyAdmin. If I try to change the collation within phpMyAdmin, I end up with garbled characters. If I do the following I can view the database without issue from within phpMyAdmin, but then my website appears as ??????.

mysqldump -uUSER -pPASSWORD database > db.sql
replace "latin1" "utf8" -- db.sql
mysql -uUSER -pPASSWORD database < db.sql

<QUESTION>
So, I can either view the characters correctly on my site, or within phpMyAdmin, but not both. There must be a step I am missing somewhere. Do I need to do something before changing the collation, or is the problem with my mysql connection?