The Collaborative International Dictionary of English v.0.48:

flat foot \flat" foot`\, flatfoot \flat"foot`\ (Med.)
   A foot in which the arch of the instep is flattened so that
   the entire sole of the foot rests upon the ground; also, the
   deformity, usually congential, exhibited by such a foot;
   splayfoot.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

flatfoot \flat"foot`\ n.
   a police officer, especially a foot patrolman. [slang]
   [PJC]

WordNet (r) 3.0 (2006):

flatfoot
    n 1: a policeman who patrols a given region [syn: flatfoot,
         patrolman]
    2: a foot afflicted with a fallen arch; abnormally flattened and
       spread out [syn: flatfoot, splayfoot, pes planus]

Moby Thesaurus II by Grady Ward, 1.0:

56 Moby Thesaurus words for "flatfoot":
   Dogberry, John Law, beagle, bluecoat, bobby, bowlegs, bull,
   camelback, cleft palate, clubfoot, cop, copper, crookback,
   defacement, deformation, deformity, dick, disfigurement, eye,
   flattie, freakishness, gendarme, gumshoe, gumshoe man, harelip,
   hawkshaw, humpback, hunchback, knock-knee, kyphosis, lordosis,
   malconformation, malformation, misproportion, misshape,
   monstrosity, mutilation, peeler, pig, private eye, shamus,
   skip tracer, sleuthhound, splayfoot, spotter, swayback, talipes,
   tec, teratology, the cops, the fuzz, the law, torticollis,
   truncation, valgus, wryneck