der Schaden
damage
A negative effect on an object that impairs its value, function, or appearance; damage.
Der Hagel hat einen erheblichen Schaden am Auto hinterlassen.
The hail left considerable damage on the car.

damage / harm
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damage
A negative effect on an object that impairs its value, function, or appearance; damage.
Der Hagel hat einen erheblichen Schaden am Auto hinterlassen.
The hail left considerable damage on the car.

The noun 'der Schaden' (damage/harm) belongs to the verb 'schaden' (to harm). An important rule is that the verb 'schaden' always takes the dative, not the accusative.
Lärm schadet den Ohren.
Noise harms the ears.
'Schaden' (damage/harm) is often combined with certain verbs. You can 'verursachen' (cause), 'anrichten' (cause/do), or 'zufügen' (inflict) damage. If you repair damage, you can 'beheben' (fix/remedy) it.
Der Sturm hat in der ganzen Region schwere Schäden verursacht.
The storm caused severe damage throughout the region.
To describe what something has been damaged on, you use the preposition 'an' followed by the dative.
Es gibt einen großen Schaden an der Hauswand.
There is major damage to the house wall.
The expression 'zu Schaden kommen' (to come to harm) means to be injured or damaged. It is often used in official reports or news stories to provide information about accidents.
Bei dem Brand sind zum Glück keine Personen zu Schaden gekommen.
Fortunately, no people came to harm in the fire.
The expression 'einen Schaden haben' (to be crazy) is colloquial and expresses that someone is crazy or unreasonable. Depending on the context, it can be joking or insulting.
Er will bei Minusgraden im T-Shirt joggen? Der hat doch einen Schaden!
He wants to jog in a T-shirt in freezing temperatures? He must be crazy!
mistake / error
'der Fehler' and 'der Schaden' can both have to do with something negative. A 'Fehler' is something that was done incorrectly, or a defect in something. A 'Schaden' is the negative consequence, for example something broken, a loss, or a disadvantage. They are often confused because a 'Fehler' can cause a 'Schaden'. But they do not mean the same thing: the 'Fehler' is often the cause, while the 'Schaden' is often the result.

Nach dem Sturm war der Schaden am Dach deutlich zu sehen.
After the storm, the damage to the roof was clearly visible.
Im Bericht hat Lisa einen Fehler entdeckt und ihn sofort korrigiert.
Lisa found a mistake in the report and corrected it right away.