The first is the mysql version. Generally, this doesn't create many hiccups but you can sometimes get incorrect results moving up to a later version if you coding uses deprecated methods. Sorry, my examples are half -baked and can't recall a specific one. :-)
The second is encoding. For example, if you use the mysql encode() or decode() functions and your original tables are set for latin1, and the default for your new database is utf-8, your queries may not return correct values. The solution is to update the tables to latin1 collation.
Other than that, using the mysql command "source" will repopulate a DB from a mysqldump file in no time flat.
We have been told to watch out for problems with some of our "columns" or tables vis a vis PHP, that we might have to copy and paste. But I can't figure out why that would be. Anyone have a clue what this is about?