How would I compare and remove hacks to core?

I have been put in charge of a site that have a lot (and i mean it) of core hacks,
some are pretty easy, some are really hard to spot (like removing a do_action on the_content.

So, my question is , how i would and remove the hacks the previous maintaners did, while adding the new features requested.

Should i go and fix as soon as i spot them, or actively search for any hack in the core? (Side-Effect of the core hacks,can not update wordpress or it will completely break and a lot of features will be “removed” effectively putting the site down)

Pull down the copy of WordPress from your client’s server to your local.

Download a clean zip of the version of WordPress your client has installed. http://wordpress.org/download/release-archive/

From there, you will need to use a file comparison tool (i.e. Diff on Linux). You can also use GIT to find the difference in folders by creating a GIT repo of the hacked WordPress, then overwrite the files with the new WP and GIT will track them and show you the differences. Github for Mac can make easy work for you.