Umm, sorry alpaca, but I beg to differ. You can hurry production by clicking on your city label, which brings up the production queue screen and so on.
In the upper right corner you've got 3 groups of stats--I can't remember what, exactly--but the first one, which is also the only one which is hidden, with just a + sign before whatever it says on it--is the one that controls that city's production focus. (How convenient, I hear you say! So nicely hidden!)
Anyway, click on it and you get a drop-down menu where you can make your city hurry production, or focus on wealth, or food, or science, etc. This is also where you can manually assign citizens to become specialists to fill empty slots in your libraries, universities, etc.
Of course, hurrying production has a bigger effect the larger the city is--it can be very powerful in your capital--always your biggest city--for churning out war units, for example. If you ally with a maritime CS it is even more powerful, because focusing on production cripples food output and often throws cities into starvation mode without the maritime CS food bonus.