
der Ausrutscher
slip
A sudden slide on a slippery surface, often leading to a fall or near fall.
Ein kleiner Ausrutscher auf dem vereisten Gehweg führte zu einem gebrochenen Arm.
A small slip on the icy sidewalk led to a broken arm.
slip / lapse
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slip
A sudden slide on a slippery surface, often leading to a fall or near fall.
Ein kleiner Ausrutscher auf dem vereisten Gehweg führte zu einem gebrochenen Arm.
A small slip on the icy sidewalk led to a broken arm.

lapse
A small mistake, a thoughtless remark, or a one-time instance of misconduct that does not match a person's usual character or behavior.
Seine unpassende Bemerkung beim Abendessen war ein peinlicher Ausrutscher.
His inappropriate remark at dinner was an embarrassing lapse.
'Der Ausrutscher' (the slip/lapse) is the noun form of the separable verb 'ausrutschen' (to slip). It describes the event or action of the verb, that is, the sudden sliding.
Pass auf, dass du auf dem nassen Boden nicht ausrutschst.
Be careful not to slip on the wet floor.
The literal meaning refers to a slippery surface such as ice or a wet floor. You can recognize the figurative meaning from words that relate to behavior or speech, such as 'Bemerkung' (remark), 'Fehler' (mistake), or 'peinlich' (embarrassing).
Sein Ausrutscher auf der Bananenschale sah lustig aus.
His slip on the banana peel looked funny.
In the literal meaning, the preposition 'auf' with the dative is often used to name the surface on which someone slips.
Ein Ausrutscher auf der Treppe kann gefährlich sein.
A slip on the stairs can be dangerous.
In the figurative meaning, 'Ausrutscher' (lapse) is often combined with adjectives like 'peinlich' (embarrassing), 'verbal' (verbal), or 'einmalig' (one-time) to describe a social or linguistic mistake.
Der Politiker bezeichnete seine Aussage später als einmaligen Ausrutscher.
The politician later described his statement as a one-time lapse.
to provide / to be mistaken
„Sich versehen“ and an „Ausrutscher“ can both refer to a small, one-time mistake. „Sich versehen“ emphasizes unintentionally getting something wrong, while an „Ausrutscher“ usually refers to an atypical lapse or thoughtless remark. For a specific oversight, „sich versehen“ is the better choice.

Seine unbedachte Bemerkung war bei der Besprechung ein einmaliger Ausrutscher.
His thoughtless remark was a one-time lapse during the meeting.
Ich habe mich beim Kopieren der Zahl versehen und eine Ziffer vertauscht.
I made a mistake when copying the number and transposed two digits.