Was my coffee actually supposed to be gritty? I was at a Middle Eastern restaurant and ordered a cup of their "Middle Eastern coffee" (perhaps something akin to Turkish coffee?), which seemed to have some sort of spice and sugar added to it. (The latter was significant only because I generally take hot coffee without sugar.) Now, after a few sips, I found that the coffee was becoming a bit gritty, presumably from some coffee grounds.

Given the general quality of the restaurant, I wouldn't be surprised if this was just bad quality. Thus: is this grittiness something to be expected from such a style of coffee, or was this probably just bad processing?
Utterly to be expected - the coffee is made with coffee grounds, sugar and water in a small tapered pot. There is no filter. If you want filtered coffee, order something else. There should be grounds on the bottom of the cup. Unless you like grounds, minimal stirring and swirling will help to keep them down there.

This is the coffee that is sometimes described as Strong as [x], Black as [y], Sweet as [z] where x, y, and z are place holders for one of love, hell and death, permuted as suits the mood.