It's a little counter-intuitive to me that all that one has to do to "select" a column or a row is to point the mouse at the square. I kept trying to click at first. Perhaps make the selection outline a little brighter or show an outline over a whole row or column to emphasize this.

Another problem that I have with the "over to select" method is that I find myself trying to move the mouse to select the next square while I am moving a square around. Of course, doing this changes the selected square.

Also, consider making starting with a slower fill speed for the early levels. :-)

You've made a very addictive game.