Petechiae or Cherry Angiomas: These are small, round, red or purple spots that appear on the skin due to minor bleeding from broken capillary blood vessels. They are very common and can appear anywhere on the body, including the feet. Given the description of small red dot clusters that are not itchy or painful, this diagnosis seems the most plausible.

Folliculitis: An inflammation of the hair follicles, which can cause small, red, and sometimes itchy bumps. However, since the lesions are described as not itchy, this might be less likely, but still possible, especially if the patient has been shaving or has had close contact with someone who has a similar condition.
Keratosis Pilaris: A condition characterized by small, rough, sandpapery bumps or patches on the skin, often on the arms, legs, buttocks, and cheeks. While it's more common on the arms and legs, it could potentially appear on the feet and might be considered if the dots are slightly raised or rough to the touch.
Pityriasis Rosea: A rash that can start with a single, large spot (herald patch) followed by an eruption of smaller spots, typically on the trunk, but can appear on other parts of the body. The spots are usually not itchy or painful but can be mildly uncomfortable.

Meningococcemia: A severe infection caused by the bacterium Neisseria meningitidis, which can lead to meningitis or septicemia. Early signs can include a rash that might initially appear as small, red, non-itchy spots. This condition is life-threatening and requires immediate medical attention.
Endocarditis: An infection of the inner lining of the heart chambers and valves, which can cause small, painless, red or purple spots on the skin (Janeway lesions) among other symptoms. This condition is serious and requires prompt diagnosis and treatment.

Leukocytoclastic Vasculitis: A condition characterized by inflammation of the blood vessel walls, which can cause small, red or purple spots (purpura) on the skin. It's a rare condition and would typically be associated with other systemic symptoms.
Erythema Infectiosum (Fifth Disease): Caused by parvovirus B19, this condition can lead to a distinctive "slapped-cheek" rash, but it can also cause a rash on other parts of the body, including the feet. It's usually accompanied by mild fever and cold-like symptoms.