Electrical – Why is there a voltage between the mains ground and the radiator

1) Why would you expect a potential difference not to appear? N and earth are tied together only in distribution/transformer boxes, that's a long way till your house, the N wire is usually carrying some current so its potential might slightly differ from ground.

2) If you call tripping the whole house an issue, well that's an issue then. I'd say that safety is not compromised at all, it is instead enforced by this behaviour. Disconnecting also the N through the circuit breaker would work.

If you have totally balanced loading on your two phases you will not be able to detect any change. EDIT: Note that this is pretty much never going to be the case.

1. EDIT: If you have a poor ground connection or the utility provider has a poor ground connection you will have a floating ground. Unless the neutral is bonded to a good local ground point it will float. It will float in potential closer to the phase that has the heavier 115V loads. If you have a 10A load on one phase and a 1A load on the other phase you may find that the 1A 115V load sees 200V and the 10A 115V load sees only 30V. Electronic and reactive devices will behave unpredictably at 200V or 30V if they are designed for 115V. Resistive loads will dissipate more or less depending on the supply voltage, over voltage will easily burn out transformers, globes and motors, under voltage will also affect electronic power supplies and synchronous motors that fail to get to speed.
2. They can will be sharing the utility neutral until the point where the neutrals is are bonded in the fuse cabinet. From this point it would be unwise to share it for reasons like you describe but I can see it happening when extra outlets are added with a mix of 115V and 230V without due supervision. EDIT: The consumer is not expected to cope with a floating utility side neutral or ground, it should never occur, in some wiring codes they are bonded in the fuze box, in others the ground is local and the neutral comes from the utility transformer common connected to the ground at the utilities transformer. Sharing an local neutral conductor between unbalanced loads is bad practice and not conformant to most wiring codes.

EDIT:

Below you can see how two dissimilar loads will cause the floating neutral point to be pulled from the earth reference if they share a neutral wire and it is compromised. In this example with the loads selected the larger load will be running at undervoltage (23V) and may survive if it is an incandescent lamp or heater but may fail if it is a motor or electronic load. The other load will see 207V and will likely suffer some failure no matter what sort of load it is.

It is also worth noting that the floating neutral point will be 92V above the protective earth, if any, in this example.

^{simulate this circuit – Schematic created using CircuitLab}