When expanding your city, there's a line which tells you that you have "X Free Tiles Remaining" (or something similar). Usually, even though I had "0 Free Tiles Remaining," I could still build new buildings.
It took me a bit to figure out exactly what tiles that was referring to - it's the 2x2-squares "building blocks," rather than the individual building squares.
Accordingly, there needs to be a better indication of which 2x2-square tiles have been claimed and are available to be built on.
Moreover, there should be a better indication when placing a building will result in you claiming a new tile. Perhaps there can be a dialog box that pops up asking if you want to expand into that particular tile, with a check box for "Do Not Show This Message Again."