Contact Dermatitis: A common condition in older adults, contact dermatitis can occur due to exposure to allergens or irritants. The fact that the rash is localized to one leg suggests a localized exposure, making this a plausible diagnosis.

Eczema (Atopic Dermatitis): Although typically seen in younger populations, eczema can persist into older age or have a late onset. The description of a raised, erythematous, and well-circumscribed rash could fit with eczema, especially if the patient has a history of atopy.
Psoriasis: Psoriasis can present with well-defined, erythematous plaques and can be localized to one area of the body. The age of the patient and the description of the rash make psoriasis a consideration.
Cellulitis: While cellulitis typically presents with more systemic symptoms and a less well-defined border, it's possible for early or mild cases to present with a more localized, erythematous rash. The fact that it's on one leg only could suggest a localized infection.

Deep Vein Thrombosis (DVT) with Associated Rash: Although DVT typically presents with swelling, warmth, and pain in the affected limb, a rash could occasionally be part of the presentation, especially if there's associated inflammation or phlebitis.
Vasculitis: Certain forms of vasculitis, like cutaneous small-vessel vasculitis, can present with a rash. Given the potential for serious complications, including renal involvement, missing this diagnosis could be critical.
Malignancy (e.g., Cutaneous T-Cell Lymphoma): While rare, cutaneous lymphomas can present with skin lesions that might resemble a benign rash. Given the age of the patient, considering malignancy is crucial, even if it seems unlikely.

Erythema Elevatum Diutinum (EED): A rare condition characterized by red, purple, or brown lesions typically on the extensor surfaces. It's associated with various conditions, including infections and autoimmune diseases.
Necrolytic Migratory Erythema: Associated with glucagonoma syndrome, this condition presents with a distinctive rash but is exceedingly rare.
Sweet Syndrome (Acute Febrile Neutrophilic Dermatosis): Characterized by fever, neutrophilia, and tender, erythematous skin lesions, Sweet syndrome is rare and can be associated with infections, inflammatory bowel disease, or malignancies.