This has bitten me in the past — basically, MySQL changed some defaults on version 4.1.
Where version 4.0 defaulted to charset latin1 and collation latin1_swedish_ci, later version defaulted to a saner charset utf-8 and collation utf8_general_ci
If you migrate it using the usual mysqldump command, you may very well get weird characters.
You’ll need to take extra care. A comprehensive article on the subject is available on Drupal’s website.
A much simpler explanation (less robust though) is available here (also detailed the way to check if you have set MySQL server correctly).
I thought this can be forgotten already, but I still found old MySQL servers from time to time. Can’t blame them, it works, so why mess with it ? But then you need to be careful when moving data to / from these old MySQL servers. And turned out finding a comprehensive article on the subject can be pretty hard (too much noise on google). So hopefully this will help someone else as well.