Japt, 14 bytes

d@sY ð_§XÃxÈ-Y

Japt Interpreter

Outputs false for BST, true for no BST.

Explanation:

d@                Run on each item X, return true if any aren't 0: 
  sY                  Ignore the numbers before this index
     ð_§XÃ            Get the indexes of numbers less than or equal to X
                          If it is a BST, then this list will be sequential numbers starting from 0
            -Y        Subtract the position within the index list from each index
                          eg. [0,1,2] -> [0,0,0] , [0,1,4] -> [0,0,2]
          xÈ          Sum the resulting array