How can I do this without separately touching up all 150 frames (layers) in Photoshop. I'm using the blur tool.
To my knowledge
There's frankly no easy way to do this. Its the nature of video and Photoshop is still pretty basic for animation. If you were using After Effects you could add a blurred layer mask over the timeline.
In Photoshop this question addresses how to blur all layers beneath it: Photoshop: how to create an adjustment layer that blurs all layers below?
Now that is only going to be really helpful if the part that needs blurring is static. If its moving around then it becomes even more complicated. Even in After Effects, much like Flash, you would have to go in and set keyframes every so often (or use Advanced Motion Tracking) to move the layer mask around.
There could be a solution someone else has come up with though