Such as the rate of decay being constant.
Such as the assumption that the sample has never been contaminated.
Such as the rate of diffusion is the same on the edge (or surface) of a sample as it is in the middle (or center).
Prove the above assumptions, and I may allow for it to be a little more accurate. The problem with all the forms of dating is that they do agree with each other within a few percent, but that's not proof that they are accurate within a few percent.
Actually is is quite easy to take care of all three of these objections at once. Simply date something for which you have a known age. Compare actual age against radiocarbon age.
Try dating sea shells collected in the 1800s and see what you get. This also gives a correction factor for deep water marine upwelling.
Try dating Greek, Roman, and Egyptian artifacts of known ages. Compare actual age against radiocarbon age.
Date trees, whose age can be established by counting tree rings. Use long-lived trees, such as bristlecone pines, and overlap the distinctive rings for older and older samples. Date a particular ring and see what you get. This technique goes back some 11,600 years currently. This allows a calibration curve to be established which accounts for all three of your objections.
By the way, the only folks who propose a wildly shifting decay rate are creationists, not scientists. And, they have no evidence other than the results of radiocarbon dating fail to agree with their young earth beliefs.
For this reason the creationist websites are not a very accurate source of information on this subject.
You still have not proved that the rate of decay has been constant through time. Sure--it's been constant for the last couple of hundred years of so. But that's all you can prove. You cannot prove that it's been at this same rate through thousands (much less millions) of years.
These assumptions may be very basic (the speed of light), or they may be very limiting ("There is no God, so how can I explain this?")