IIRC Hertz/Frequency
Really only comes into play if the appliance also has a motor and or today computer/electronic controls. Older European appliances that had mechanical timers were brougth to these shores and apparently used (if those that show up on eBay and elsewhere are any judge), with little to nil effect. That being said one assumes some motors are more sensitive to being used at faster or slower frequency than listed on the rating plate. There is also many appliances right through the 1970's or so were designed with motors that could run on 50hz or 60hz.
Miele USA once explained to us why American appliances designed for 220v cannot run on "European" power of the same voltage and often vice versa. Much of it has to do with how Americans get their 220v power (two 120v lines) versus Europe (a single 220v line and neutral (IIRC)).
Then there is also many American appliances even if rated for 220v have parts that run on 120v power so need both.
On the otherside European appliances that require 220v power can often be run off American 220v system,again if the frequency difference does not cause problems. You can even run them off a voltage converter (step-up 120v to 220v) long as the total power draw does not exceed the rating for the converter and circut the power is being drawn from.
Awhile back a company in Canada (EuroLine) sold AEG washing machines and dryers to the North American market. Though they ran on strict 220v/50hz power Euroline provided installation directions (they shipped the things south to the USA,one had to take things from there)and IIRC posts over on THS/Appliance forum more than a few were sold and the units worked fine.
My Pfaff ironer was brought to these shores from Europe by the previous owner's mother and used until the day we made the purchase. It was connected to and has an American 220v "dryer" plug. We had a serviceman frm Germany out a few years ago (don't ask, long story) and he showed us how to adjust the roller speed to compensate for the faster rotation caused by using a 50hz appliance on 60hz. Have had the unit for over ten years now and it works perfectly fine. Pulls nearly 3000 watts of heating/steam producing power, but ....
EU/UK laundry and dishwashing appliances and cold water:
One reason for 220v or even 408v power grid being built for homes in that area of the world was mainly because it was a given laundry and later dishwashing appliances would have to heat their own water. Indeed for much of modern history hot water is provided for such areas by instant heaters located near or in the kitchen, bath or where required. Contrast this with the United States where central boilers/hot water tanks supply homes and buildings with heated water.
It was also far easier to retro-fit many of the old (if not down right ancient)housing stock with electrical wiring for either appliances or water heaters as opposed to running hot water pipes from a central water heating system.
Boil washing didn't start being attacked/dying out in Europe/UK until around the 1970's or so with the "energy crisis". Until then it simply was a given housewives wanted that feature on their washing machines, so the power had to be there to provide.
Finally here is allot of debate on how it is more efficient for a washing machine or dishwasher to heat it's own water versus using that from a central supply. This is not always so and depends upon many factors.
Before safety and other concerns caused water heater temp changes here in the USA, it was quite common to get water >140F or even 160F from tanked or tankless hot water systems. Rudd and others advertised this feature for housewives showing all the new modern appliances (dishwashers, washing machines etc...) that required lots of hot water, but the supply also had to be great so His Nibbs and the children could take their baths.
Depending upon costs of heating the water and other factors such as temperature loss due to distance travelled, it is not always cheaper to have an appliance that can heat tap cold water to warm, hot or boiling.
Consider also with modern enzyme and bleach laden dishwashing and laundry detergents much of the argument for starting from tap cold water and heating to warm or hot is lost.
Blood amoung other substances that create stains is actually set when exposed to cold water. Commercial laundries use warm water (with or without alkaline chemicals) to flush such stained laundry before it is washed. Such places at least on this side of the pond also use several changes of wash water at temps ranging from 100F to over 150F that occur so quickly there wouldn't be time to heat water unless one uses some very powerful heating elements (steam fed washers for instance).
Keep in mind that while a washer or dishwasher is heating that water the detergent is already working. When this heating time is added to the actual wash time you'll often find things are clean long before the set temp is reached or shortly afterwards. In the case of laundry the remaning time is simply beating the wash back and forth.