What sorts of appliances will malfunction or worse, potentially harm someone, if plugged into an outlet that is wired backwards?
In the real world, people do die from this, alas.
Modern appliances are EITHER double insulated or have a safety ground.
Double insulated is more a level of insulation than two physical layers of insulation. DI means that the appliance is never electrically unsafe under regulatory acceptable conditions of use. If you eg stand in a puddle while holding it and pour water into it, or use it while in a bath or shower, you may exceed the regulatory conditions of use envelope.
A safety ground is an arrangement that connects accessible or modestly insulated metal parts of the appliance to system (in this case "usually" house) ground. If an electrical path develops between supply "Phase" and the earthed metal parts, ground current will flow and curcuit protection will operate (fuse or circuit breaker). Systems with resdiual current tripping (named variously ELCB/GFI/RCD) devices can detect very small currents to ground (<= 20 mA) and discnnect the circuit in <= 1/2 a mains cycle.
The mains feed consists of two wires - usually termed Phase and Neutral .
Neutral is usually held at ABOUT ground potential but is NOT connected to the ground lead within the appliance. Phase and Neutral can usually be reversed at the appliance feed point without causing immediate hazard. In a DI appliance there is minimal effect. In a grounded appliance there SHOULD be minimal effect.
If neutral and ground are connected within the appliance it will still usually operate but large metal parts connected to ground will now be at neutral potential. This may affect the ability for house fuses or breakers to operate correctly and WILL trip residual current devices.
Any appliance which has the earthed metal parts connected to Neutral (which they should not have) will have the metal parts placed at phase potential if feed PN are reversed. If the metal parts are a toaster or electric jug or vacuum cleaner or ... body then this may be a very very very bad idea indeed.
If an appliance cord is wired incorrectly, strange things may happen, or it nothing obvious may happen but trhe appliance may become letally dangerous. Long long ago I was asked to investigate a situation where there was a house with an external sleepout. Most appliances worked OK in the house or the sleepiy but a casette recorder would only work in the hpuse but not in the sleepiut. Investigation revealed that
the sleepout had P & N reversed, and
the tape recorder has N & E reversed.
Usually this would be a relatively benign fault.
In this case most appliances saw N-P rather than P-N, E was OK so they worked OK.
However the tape recorder saw N-E on what should be P-N so did not work.
s has Phase on it's earth pin and the whole body was live at 230 VAC. What saved people was probably that the sleepout had no major grounded metal and, as the TR did not work when plugged in, people spent little time touching it.
So close !
Swapping phase and neutral may result in the appliance "internals' being live when it is turned off.
I'm in NZ. The mains supply is 230 VAC, 50 Hz. I note informally only that it seems that with 230 VAC people seem to care somewhat more about shock hazards that with 110 VAC. I've seen practices in other countries which would be utterly unallowed on NZ.
An important aspect of swapping phase and neutral is when the appliance has a single pole switch. This can only 'break' ne of the two mains leads and it is invariably designed to disconnect the phase lead. If P & N are swapped the Neutral lead is disconnected and the appliance will not operate BUT the Phase lead is connected to the equipment internal circuitry. The chances of an accident are significantly increased.
Some equipment is required by law to disconnect bot leads when switched off. An excellent example is an electric toaster where, if P & N were reversed, a single pole switch would cause the element assembly to be at phase potential.
Some years ago a batch of Chinese manufactured toasters that allowed a single leadswitching fault to occur were imported to NZ. The fitted two pole switch could have one of its two "fingers" trapped against an insulating mount of not properly assembled. As the toaster still switched off thermally if either lead was broken this fault was missed by the manufacturer and importer. About 5% to 10% of the toasters has phase on the element when turned off. This was brought to my attention when an adult nephew did what I would not have done in my wildest dreams (hopefully). He picked up an "off" but plugged in toaster to move it by inserting fingers down the two slots to grip the middle bar !!!!!!!!!!!!!!!!!!!!!!!!!! . Shocking!. The importer was somewhat cagey. I lashed up a capacitance based tester that could tell if either witch pole was stuck closed. In such a case the element to body capacitance was far higher than when both poles were opened - plug toaster 3 pin plug into the capacitance tester and voila! A trip through a few showrooms revealed the extent of the problem and an appliance recall resulted.
Caravans, campers ... supplied power via mains lead:
In many countries Caravans require a neutral earth link in their in-van switchboard. This is safe if fuses or breakers are installed in the caravan and will work with fuses or breakers in the feed switchboard. RCDs in the feed switchboard will trip if this link is in place. Removing the link stops remote RCDs tripping but then the caravan MUST have RCDs as well.
SO - If P&N are reversed on a caravan with a van N-E link then the van will now have a P-E link and will blow supply fuses. BUT if the supply ground is faulty the van chassi and metal parts will be at Phase relative to ground. Properly wired appliances will work OK.
Stepping in and out of the van WITHOUT providing a ground to caravan metal bridge with your body will not cause a problem.
But if you bridge van metal to ground with your body you will receive a full mains shock. You may die and people have died in just this situation.
Removing the in-van N-G link will prevent this shock hazard but then the fusing may not work correctly and eg fire may result and [all together] you may die. Or your family.