Are there long-term effects of athlete's foot?

Cellulitis. Chronic athletes foot can cause cracks in the skin which can spread to the nails causing thickening and disfigurement of the nails. In others bacteria can gain access and develop infection of the lymphatics causing swelling- an infection called cellulitis. This requires antibiotics. If the atheletes foot is not cured cellulitis can recur.
Rarely. The fungal infection causing athlete's foot is annoying, but unless there is a secondary bacterial infection , will not generally cause any long term problems.