I’ve got a major, concrete reason Dreamhost needs to upgrade MySQL.
MySQL 5.1 supports utf8 encoding, but not the newer utf8mb4 encoding. You need the latter to store four-byte Unicode characters, including all emoji. A utf8 table will truncate all input into a field after any four-byte characters in it. So if someone uses an emoji, which is a very common use case these days, it will cause significant data loss. Which I’ve just experienced on a site I just upgraded to use UTF-8.
I’m seriously considering moving this site away from Dreamhost for this reason, and I bet I’m not the only one.