I've been having problem being able to get my palm muted picking consistent and quick. I can downpick for riffs that aren't palm muted eg. Master of Puppets intro, but when it comes to just constant palm muted picking I find that I can't keep the same speed for long.

Also I find that I seem to add in another note when trying to keep the same speed.

The song I discovered this problem in was "Want You Bad" By "The Offspring" Just after the intro it's a series of palm muted picks and I just can't get it consistently fast.

Any ideas on how to build up speed/consistency when doing this?

Ummm.. Master of Puppets is palm muted twice on then once off.
Consistency and quickness are two problems with one solution : practice

Palm muting is a rather tricky technique , and here's my humble advice :

Try palm muting in general , with chords , barre chords etc ... until you get the right sound without too much effort ...

As for songs , make sure you're not pressing the strings too much with your right hand , and just practice riffs very slow , slow enough that you get every single note correct , and then start speeding up your tempo ...

Eventually , your practice will pay up , and you WILL post your cover on your profile page ...
PS : English is not my first language