When using dye you need to, clean the whole bottom of the car, run it right after putting the dye in it, and look at it with the UV light. If left in there for an extended time, the air flow under the car spreads it all over, making it next to impossible to find the source of the leak, speaking from experience.
In my dealings with using dye, there are no ill effects from leaving it in the lubricant. We didn't drain it out after the initial investigation to find the source of a leak. As far as what we used in dealerships, there was no need to drain it.
Mike Garblik says that the smoke machines work much better than dye does, so even though I've never used a smoke machine, I tend to believe him. The dye is less than easy, or foolproof for finding leaks. Sometimes you can clearly see the source, but not always as if you don't use the light at the exact right time, it can give you misleading information as it spreads.
Many times I've just cleaned the bottom of the car, the have someone run the car on the lift, that way there is little air current moving the lubricants around, maybe a little from the fan, but nothing like when the car is running down the road at 55 MPH. No dye, just watching for the leak to show itself by the first drips. Even in a dealership, this was how we identified 99% of the leaks, we seldom used dye.
