They don’t just poop on surfaces, they also leave “fecal spots.”
These brown, semi-liquid deposits from their rear end contain pheromones that attract other roaches to the site. You can find fecal spots in tight spaces and cracks and crevices where cockroaches hide such as behind pictures on walls or in the space along kitchen cabinet hinges (see Cockroach Fecal Spots Attract Other Roaches).

They walk across disgusting things…and then your kitchen counter!
Cockroaches walk across and feed on all manner of disgusting things: pet poop, baby diapers, garbage, their own feces, where they pick up various bacteria and viruses on their legs and antennae (just like house flies) and then transfer them to your food, dishes, and other surfaces. Cockroaches have been known to transmit Salmonella and other diseases to people in this manner (see Can Cockroaches Really Spread Diseases?).

They sometimes turn into soft, white, helpless roaches.
Cockroach nymphs must shed their hard skins several times in order to grow to become adults. Their old skin or cuticle splits open and reveals a soft, whitish, slightly larger, roach underneath. These so-called “albino” nymphs are rarely seen since they remain hidden for several hours while their new cuticle hardens and turns brown (see Cockroach Nymphs Leave Their Shed Skins Behind).

Their many babies are protected inside a portable egg case.
Females produce a leathery, oval egg case or capsule that can contain as many as 48 little roaches. They deposit the egg case in a hidden, protected place where you can’t find it, but where it will hatch out hours or weeks later. Cockroach egg cases also survive insecticide applications, so just when you thought you were finally rid of roaches, a whole new crop can hatch out (see Cockroach Egg Cases Are Hidden).

Their poop, shed skins, empty egg cases, and dead bodies can cause asthma.
People can become sensitized to cockroach parts that can become airborne allergens. Cockroaches cause more asthma issues for inner-city children than dust mites or pet dander. Eliminating the cockroaches and even thorough cleaning usually fails to remove all of the hidden allergens (see Cockroach Allergen is a Very Real Problem).