Changing the Application Master Page

Some system files (for example EditProfile.aspx in My sites) have a hard coded url to the application.master page:

MasterPageFile="~/_layouts/application.master"

If you'd like to use your own master page, you'd have to change this to the following:

DynamicMasterPageFile="~masterurl/default.master"

And FYI changing these system files is technically unsupported, but I've often found it's sometimes a necessity.