If you want to know the number of unique properties of Objects in an Array, this should do it...
var uniqueProperties = [];
for (var i = 0, length = arr.length; i < length; i++) {
   for (var prop in arr[i]) {
       if (arr[i].hasOwnProperty(prop) 
           && uniqueProperties.indexOf(prop) === -1
          ) {
          uniqueProperties.push(prop);
       }
   } 
}
var uniquePropertiesLength = uniqueProperties.length;
jsFiddle.
Note that an Array's indexOf() doesn't have the best browser support. You can always augment the Array prototype (though for safety I'd make it part of a util object or similar).