What situations are pressure cookers not appropriate
By raising pressure, you get water to boil at a much higher temperature and thus speed up most of the physical and chemical reactions involved in cooking. Elevated pressure can play a smaller role too.

With higher temperatures, you can get faster caramelisation for instance which may not be desirable in some foods, dull and/or dark colours and bitterness are two properties that come to mind (bright green pea soup gets dull for example) With lower pressure rating cookers (below 15psi or 1 bar), there is less risk of runaway browning. 

Another issue is with foods that either need fairly precise cooking or are prone to get overcooked. There is no easy way to open the lid to monitor or halt cooking abruptly. Related to this is the inability to stir and a very real risk of food getting stuck and then burnt even when there is still plenty of liquid (as it just happened to me moments ago). Heat control cannot always be casual.

Whatever you put into it, should either have a high water content (70% or so) or you need to maintain a certain amount of free water for it to work. I find that often I needed to use extra water and drain it off after cooking; that may not always be desirable. Making pet food for example can be awkward as you do not really want to get rid of the free liquid which has plenty of nutrition in it. You can work around it by putting your food in an elevated container and pressure steam it although you still tend to get free liquid from condensates in the container.