1. The rate of decay remains constant.
This isn't an assumption. We have evidence that decay rates have been constant for at least the last 2 billion years. There's no evidence that rates vary under ordinary circumstances, or circumstances that would leave no other evidence.
2. There has been no contamination (that is, no daughter or
intermediate elements have been introduced or leeched from the specimen
of rock).
Not an assumption. Contamination would leave evidence that we could detect.
3. We can determine how much daughter there was to begin with (if
we assume there was no daughter to begin with, yet there was daughter at
the formation of the rock, the rock would have a superficial appearance
of age).
Not true. Not all radiometric dating requires zero original amounts of daughter isotope, apparently.
That's about all I know. I'm no scientist but that's what I've picked up from the board. As for the helium stuff I'm pretty sure that's been refuted before...
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