To be clear, though, slowed can still affect things like an action that lets you shift your speed or the run action.
I don't have the books in front of me, but I'm pretty sure that the run action lets you move your speed plus two squares. So, running while slowed would let you move four squares since your speed is two.
Also, a power like Tumble which, post-errata, lets you shift your full speed will only let you shift two squares while slowed since your speed is two.
Now, if you had a power that specifically said, "Shift six squares," that would be unaffected by slowed. For instance, a Pursuing Avenger with a Dex modifier of +3 who used Angelic Alacrity (before the attack, shift a number of squares equal to 1 plus your Dex modifier) would still be allowed to shift the full four squares since the power doesn't refer to your speed anywhere.
At least, this is how I interpret the slowed rules.