Those are hard questions to answer generally, which is perhaps why there have been no takers, until now, that is.
I can make a high yeast dough using warm water that is fermented at room temperature that will start to go south after a couple of hours, or I can make a low yeast dough using cooler water that is cold fermented and last over two to three weeks (in the refrigerator). Unfortunately, the signs that a dough is going bad will vary depending on the type of dough and how it is managed. For example, a dough with a lot of yeast might rise and then start to collapse, and that would be a good indication that the dough is either past its prime or about to become unusable. Such a dough might also have a large profusion of small bubbles, which can often be seen at the sides and bottom of the dough (if you are using a glass or a transparent plastic container). If very large bubbles form in the top surface of the dough, say, about the size of a nickel or larger, that is another possible sign of overfermentation. But that isn't always the case, especially if the dough is otherwise firm to the touch. It the dough blows the lid off of its container and then starts to overflow the container all over your counter, then that is not a good sign.
A dough with a small amount of yeast, or possibly a natural starter or preferment, might also produce bubbles but perhaps not as many or it may take longer for them to appear and, at the same time, the surface of the dough may start to take on a gray color as it ages, with a lot of spots (they are harmless). Even then, the dough may still have a few more days before becoming unusable. In cases like this, I press the dough with my finger and if the dough is still firm, it is likely that it still has some time left before using.
If a fermenting dough also produces a lot of odors, especially musty odors or strong odors of alcohol that become most evident when you remove the lid of the storage container, that is also an indicator of long fermentation and that you might want to use the dough fairly soon. However, there are some doughs with large amounts of yeast, such as doughs for cracker style pizzas, where strong fermentation flavors can be desirable.
In line with what Craig mentioned, if a dough becomes wet, damp or clammy, that is another possible sign of overfermentation. Such a dough will also tend to be highly extensible (stretchy) and have a tendency to develop thin spots or tears when stretching out to size. To the extent that a workable dough skin can be formed, the finished crust is likely to be light in color, with poor oven spring, and quite chewy and crackery rather than soft. It might have good crust flavors because of all of the fermentation byproducts, but that may be the only positive.
Generally you learn through experience. Each type of dough can have its own lifespan and vital signs. There is no generic advice that can be readily applied to every dough with confidence.