Recently had a prescription error with my two month old baby. The doctor prescribed 7 times as much iron supplement as they intended (confusing labelling - so while I'm annoyed, I can see how it happened). This went on for a month until we uncovered the error.
We had blood test done (on the doctor's recommendation), and luckily there is no sign of any damage, but prescription errors do happen (even if they are rare) and it's much easier with liquids (you probably wouldn't give 8 pills to a baby, but 8ml doesn't seem so bad).
Paracetamol pills are labelled by age (and weight), available over the counter. So quite often we tend to under dose our child as children grow fast.
There's no “as in Europe”, every European country is different. In France the default is also liquid form, but the pipette is graduated is kilograms of baby weight, which limit the errors you can make (you know your kid doesn't weight 15kg when his weight is around 8).
I think the mistakes also come when the child spits out part of the liquid, and parents give another dose.