The Collaborative International Dictionary of English v.0.48:

gumshoe \gum"shoe\ n.
   1. A detective; a private eye. [slang]
      [PJC]

   2. A shoe made of rubber, as a rubber overshoe.
      [PJC]

   3. A sneaker[3].
      [PJC]

WordNet (r) 3.0 (2006):

gumshoe
    n 1: someone who is a detective [syn: dick, gumshoe,
         hawkshaw]
    2: a waterproof overshoe that protects shoes from water or snow
       [syn: arctic, galosh, golosh, rubber, gumshoe]

Moby Thesaurus II by Grady Ward, 1.0:

66 Moby Thesaurus words for "gumshoe":
   Dogberry, John Law, Sherlock, Sherlock Holmes, beagle, bluecoat,
   bobby, bull, cop, copper, couch, crawl, creep, dick, eye, flatfoot,
   flattie, fuzz, gendarme, go on tiptoe, grovel, gumshoe man,
   hawkshaw, heat, inch, inch along, investigator, lay wait,
   lie in wait, lurk, nightwalk, officer, pad, peeler, pig,
   plainclothesman, police officer, private eye, prowl, pussyfoot,
   scrabble, scramble, shadow, shamus, shirk, sidle, skip tracer,
   skulk, sleuth, sleuthhound, slink, slip, snake, sneak, spotter,
   stalk, steal, steal along, tec, the cops, the fuzz, the law,
   tippytoe, tiptoe, worm, worm along