I would say *always* use water from the COLD water tap. As long as the overall temperature of the tank does not drop by more than 3°C then that's fine. I'd say up to 40%to 50% water changes are therefore OK.
Boiled water problems are:
Using boiled water to raise the temperature of cooler water with fish: I remember reading somewhere that it can give fish problems much akin to divers who come up to the surface too quickly and get the bends.
Don't agree with that one. The primary reason boiled water is bad is your second point below, there is usually significantly less oxygen in boiled water than normal tap water. Now, if you are only chaning 5-10% it is probably not an issue, but more than that and I wouldn't chance it. The fishy-bends come from using water that is too cold and it warmed up too quickly in the tank. Then gas bubbles may form as the warmed water cannot hold as much gas as the cooler water. The real danger here is a gas bubble forming on the fish's gills. This is similar to the bubbles that form during decompression sickness a.k.a. the bends. Though, it is a rather poor analogy as this is a temperature issue with bubbles outside the fish's body and decompression sickness is a pressure issue with bubbles inside the body.
Boiled water has little oxygen in it.
I agree with this, as I said above.
Boiled water has no buffering capacity as the calcium which forms the buffers has been 'boiled' out. Over time it could lead to low KH levels in the tank and eventual pH crash.
This one I strongly disagree with. If anything, the remaining water has more calcium in it, since what you boil off is almost 100% pure water. Definitely what gets boiled off has far, far less minerals than the tap water. I definitely have quite a calcium layer on the inside of my kettle. Unless you were capturing the steam and re-condensing it... that water would have little to no buffering capability.
Just one thing that I'd like to add. A temperature change of a few degrees really is ok for the fish. Many times it triggers other interesting behavior. My cory catfish start a breeding event sometimes after I use some cold water in their tank.
It is also important to note that your fish cannot get ich or any other disease just from a temperature change. A large temperature change can lower their immune systems, and if the tank has a disease in it -- maybe at a non-symptomatic level -- the disease can then take hold, almost like it appeared out of nowhere. But, the disease HAD to be in the tank, it cannot just spontaneously appear because of the cold.