der Kot
feces
The solid or semi-solid waste excretions from the intestines of humans or animals; fecal matter.
Pass auf, dass du nicht in den Hundekot auf dem Gehweg trittst.
Be careful not to step in the dog feces on the sidewalk.

feces / dirt
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feces
The solid or semi-solid waste excretions from the intestines of humans or animals; fecal matter.
Pass auf, dass du nicht in den Hundekot auf dem Gehweg trittst.
Be careful not to step in the dog feces on the sidewalk.

The meaning 'Schmutz' (dirt) or 'Schlamm' (mud) is outdated and is now used only in historical texts or certain dialects. In modern Standard German, 'Kot' (feces) almost exclusively means fecal matter.
Beim Wandern im Wald muss man aufpassen, wo man hintritt.
When hiking in the forest, you have to watch where you step.
'Kot' (feces) is a direct, biological term. It is not vulgar, but it is often avoided in polite everyday language or replaced by a paraphrase.
Der Tierarzt untersuchte eine Probe des Kots.
The veterinarian examined a sample of the feces.
The word is often used in compound nouns to specify the source, for example 'Hundekot' (dog feces), 'Vogelkot' (bird droppings), or 'Katzenkot' (cat feces).
In vielen Parks gibt es spezielle Tüten für Hundekot.
In many parks there are special bags for dog feces.
crap / manure
'der Mist' and 'der Kot' both have to do with excretions, but they are used differently. 'Kot' is the general and rather factual word for solid or semi-solid waste from humans or animals. You often hear it in medical, biological, or factual contexts. 'Mist' means the excrement of farm animals, often mixed with straw, especially on a farm and as fertilizer. Learners may confuse the words because both can refer to bodily waste. For a medical description, 'Kot' is more precise; for fertilizer from the stable, 'Mist' sounds more natural.

Die Ärztin untersucht den Kot, weil der Hund krank ist.
The vet examines the feces because the dog is sick.
Der Bauer verteilt den Mist im Frühling auf dem Feld.
The farmer spreads the manure on the field in spring.