The original post isn't quite correct, though almost.
The bug is that once a single building is placed on an empty plot and you leave the construction menu, the game counts that plot as "full" and does not allow you to build anything else on it even if there is room.
For a quick test, start a game and queue 2 houses, each on a different plot (map grid). When you leave the construction menu it'll only show the demolish option and won't let you place anything else.
It doesn't have anything to do with starting new cities, though. In your first city leave one plot completely empty, then start a new city. You'll still be able to build in the empty plot of your first.