I don't want to contradict JasonH... he is the king here....
but I had a couple things to add.
You do not want to connect the radar detector to the yellow wire. That's energized all the time. The detector won't turn off. You want to connect the detector's power to the red wire, then it will turn on and off with the key.
While Jason is correct that it will be protected with the fuse of the fuse block, it might be a 15 amp or 20 amp fuse. The Valentine 1 has a 1 amp fuse. You might want to leave in that just for added protection. But I have left out smaller fuses on stuff like that relying on the larger fuse in the fuse block. It won't hurt anything and should protect the Valentine in case of a major problem. But a 1 amp in there after the car's main 15 amp will give you a little more protection (I would guess). Not that I can think of a problem that this would make too much difference. Generally people worry about the wire braking and shorting to ground. But if there is an internal failure in the Valentine and it draws 2 or 3 amps, the car's main fuse will let it draw that and possibly damage more in the Valentine than if there was also a 1 amp right next to it. Just a thought.
The other thing is that I don't know if the Valentine 1 has a mute output wire. Jason is right that the Z1 won't mute the Valentine 1. But I don't know if the Valentine 1 has any output wire that you could use to mute the Z1. The Z1 has a wire that you can hook to that when you do something (either ground it or put 12V on it... I can't remember which) it will mute the Z1. Problem is getting such a wire out of the Valentine 1. Does it have it? I checked the web site real quick and didn't find anything. You might want to email customer service at Valentine. Ask them if there is a wire coming out of it that you can use to mute a stereo when it detects a bogey.