Solution: 23

Written by Sofiya Vasina

The solution to the cross sum is not quite unique; in

   5487961
  32 352 39
  51 79  58
7986 62 3268
17 4 9  1 79
58 362 32 364
    1   5
312 23 249 97
 89 4  4 5 86
 4..3 23 3125
  ..  61 89
  62 857 68
   9861547

one can replace the two-by-two square of dots above with either

87    78
76 or 85

to obtain a valid solution. In either case, if we "look out for 2 3" as instructed, we find that the 2's and 3's form the following pattern (using # for 2 and 3 and . for all other numbers):

   .......
  ## # # #.
  .. ..  ..
.... .# ##..
.. . .  . ..
.. #.# ## #..
    .   .
#.# ## #.. ..
 .. .  . . ..
 ...# ## #.#.
  ..  .. ..
  .# ... ..
   .......

Interpreting # as "dot" and ## as "dash" and reading each row with #'s in it as a Morse Code letter, this gives us the solution, BAFFLE.