Plumbing. Electricity.

[Rita Winston]

No: HPFGUIDX 1542

IIRC Hermione told Harry in GoF (in reference to 'bugging') 
that electricity and electronics cannot work around Hogwarts 
because the magical field is too intense. (OH!!! Perhaps that, rather 
than nostalgia, is why the Hogwarts Express is a steam train? 
Boiling its water with magic rather than with coal?)

The Muggle Studies homework essay "Why do Muggles need electricity?" 
suggests that the wizard folk believe that Muggles have to invent 
ways to imitate the things wizards do by magic and therefore invented 
electricity, internal combustion engine, gas light, steam power, wind 
mills, water mills, because Muggles don't have candles and hearths 
that burn without fuel and can't make an object move without using 
some kind of energy from a power source (muscle power, etc) and so 
on. (Does magic violate the Laws of Thermodynamics? BROOKS???)

According to that theory, the wizards might have had flush toilets 
and baths with hot and cold running water since Atlantis, and both 
Roman and modern plumbing are attempts by Muggles to imitate what a 
Muggle visitor saw in a wizard home, just as gas light was a way to 
imitate the wall-sconce candles that light automatically when an 
authorized user enters the room, and bicycles and automobiles are 
attempts to imitate self-moving carts or chairs which we readers 
haven't actually seen.

On another tentacle, my vague understanding of plumbing is that, 
except for heating the hot water, it's all done by storing the water 
in a high enough tank that gravity is what moves the water through 
the system, and physical plugs that are mechanically put in place and 
removed are what stops it from moving. No magic is needed except to 
heat the hot water, refill those prefects' bathroom taps with their 
sweet lotions, and elevate the water into the storage tank. 

So it didn't need wizards to invent it. Actually, I kind of think  
that if wizards HAD invented wizard plumbing, it wouldn't have pipes 
running through the walls, it would have either creation  of water at 
the tap end and destruction of water at the drain end (why not create 
water at the tap end? Just change a never-empty pitcher of wine 
into a never-empty pitcher of hot water! A known technology!) or the 
water would move through the system by teleportation rather than by 
hydraulics.

Which suggests that the wizards copied their plumbing from Muggles, 
not until after Muggles had invented it, and just added a few fancy 
touches. As they presumably did with with steam trains and 
photographs and clocks. Perhaps they just aren't very good at 
inventing anything really NEW.