I reached the following position with White (after 25. ... Rfe8).
Here I played 25. Rg1, thinking I'd bring another piece closer to the attack with tempo. However, I missed a much more fierceful move that would have achieved the same. Therefore, when evaluating an advantageous position, perhaps one should stubbornly look at each of your attackers in turn and consider every legal move you have, including captures. You don't even need a deep calculation; simply place each attacking piece on the squares in your mind, one after the other.
This, of course, works only in longer games. As for a "sixth sense" of tactics -- the Knights Errant believe the Holy Grail of tactics recognition is Michael de la Maza's Circles.