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#APL (NARS), 104 characters, 208 bytes

{3≠+/⍵='.':0⋄4≠↑⍴w←(⍵≠'.')⊂⍵:0⋄∼∧/{''≡⍵∼'0123456789'∩⍵}¨w:0⋄(↑∘⍴¨w)≢1+⌊{⍵≤0:0⋄10⍟⍵}¨m←⍎¨w:0⋄256≤⌈/m:0⋄1}

The input has to be one string...test

  p←{3≠+/⍵='.':0⋄4≠↑⍴w←(⍵≠'.')⊂⍵:0⋄∼∧/{''≡⍵∼'0123456789'∩⍵}¨w:0⋄(↑∘⍴¨w)≢1+⌊{⍵≤0:0⋄10⍟⍵}¨m←⍎¨w:0⋄256≤⌈/m:0⋄1}
  a←'1.160.10.240' '192.001.32.47' '1.2.3.' '0.00.10.255' '1.2.$.4' '255.160.0.34' '.1.1.1' '1..1.1.1' '1.1.1.-0' '.1.1.+1' '1 1 1 1' '1' '10.300.4.0' '10.4F.10.99' 'fruit loops' '1.2.3.4.5' '0.0.0.0'
  {'[',⍵,'=',(p ⍵),']'}¨a
[1.160.10.240= 1 ]  [192.001.32.47= 0 ]  [1.2.3.= 0 ]  [0.00.10.255= 0 ]  [1.2.$.4= 0 ]
[255.160.0.34= 1 ]  [.1.1.1= 0 ]  [1..1.1.1= 0 ]  [1.1.1.-0= 0 ]  [.1.1.+1= 0 ]  [1 1 1 1= 0 ]
[1= 0 ]  [10.300.4.0= 0 ]  [10.4F.10.99= 0 ]  [fruit loops= 0 ]  [1.2.3.4.5= 0 ]  [0.0.0.0= 1 ]

Some explanation:

"If string ⍵ has number of points '.' different from 3 then return 0": "3≠+/⍵='.':0"

"Build the array of array of characters w cutting where there is the char '.' from ⍵; if len w is not 4, return 0": "4≠↑⍴w←(⍵≠'.')⊂⍵:0"

"If each element of w has some non-digit character then return 0": "∼∧/{''≡⍵∼'0123456789'∩⍵}¨w:0"

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