UpgradingFAQ
This covers upgrading from older versions of MySQL, and possible issues you may run into.
[edit] How do I upgrade from MySQL 3.23 to MySQL 5?
MySQL recommends a gradual update, as opposed to a direct one. See http://dev.mysql.com/doc/refman/4.1/en/upgrade.html which covers upgrading from 3.23 to 4.0 and 4.0 to 4.1, and http://dev.mysql.com/doc/refman/5.0/en/upgrade.html which covers going from 4.1 to 5.0. Do always remember to get backups (ref: BackupFAQ)
[edit] Do problems between a 4.1 client communicating with a 5.0 server exist?
From the Upgrading from MySQL 4.1 to 5.0 manual page, you'll notice that in the C API, the DECIMAL data type may cause problems. If an error such as 'Using unsupported buffer type: 246' is seen, the solution is to relink the application with the client libraries of 5.0.