Local copy of WP gives me weird characters

I host my WP site on Media Temple. They run MySQL 4.1. I like to download database dumps and then import them to the local copy of my blog as a backup. I use a Mac with MAMP (PHP 5+ and MySQL 5+).

The problem is that the local copy always shows weird characters. Instead of apostrophes and quotes, I get something like “didn?t”.

Why do I get these weird characters and how do I get rid of them? I’ve tried everything. I followed the codex instructions exactly (including which checkboxes to tick) and made sure that import with UTF-8 and MySQL 4.0 compatibility mode (and all other combinations I can think of).

Appreciate it if someone could please shed some light on this for me.