Iterate through the array in reverse so that the array does not reindex with each splice.
var arr = [['1','2','3','0'],['2','3','4','1'],['3','4','5','0'],['4','4','5','1'],['5','4','5','0'],['6','4','5','1'],['7','4','5','0']];
var arrLength = arr.length;
while(arrLength--){
if(arr[arrLength][3] == 1){
arr.splice(arrLength,1);
}
}
console.log(arr);
JS Fiddle: http://jsfiddle.net/L5T9k/