The main way to check how close you are to the happiness limit is to compare the number of

faces in a city vs. the number of

faces. This can be done on the city screen itself, or from the city menu (the one which shows stats on all your cities at once). If the city goes over the happiness limit, a

face will appear on the city bar on the main screen and smoke will rise from the city.
If you have more

than

in a city, the difference is how many non-working citizens you have there (i.e. having 6

and 8

means you'll have 2 slackers) On the city screen, there's also a line under the Specialist area that has a red-clad guy for each non-working citizen there.
As for effects on production, non-working citizens do nothing for your city. Add happiness, and those citizens will be able to become specialists or start working tiles, adding Food, Hammers, Commerce, etc. to the city. If you aren't going to be able to get any happiness to the city anytime soon, it's better not to let it grow over the limit in the first place, since the citizens who actually *do* work will have to divert from Mines and Cottages in order to feed the slackers.