There's a range of potential things that could develop, like fungal infection, clogged pores, bacterial infection in unknown cuts, etc. Likelihood depends on a number of factors.
This is relatively unlikely at Pole. While you aren't supposed to take regular showers, you're still expected to maintain general hygiene - hand washing, sponge/cloth baths on other days. If you had a cut that was serious enough that you'd worry about infection then you would probably visit medical anyway. Otherwise clean the wound and bandage as you would otherwise.
Trench foot? Athlete's foot? Ringworm? Ingrown hair picked and infected with staph from fingernail? Sure you can deal with it, but regular cleaning is the best way to avoid a problem.
