Part of it depends on what you are planning to do with it. using it to make fine furniture, the limit is much earlier than if you are going to use it for more artistic pursuits such as turning bowls or making panels from the spalted wood for beautiful accents.
For me, how I go about it is I have my chain saw handy (I'm often making firewood when doing this so nothing really goes to waste). I'll start at one end or the other and cut firewood sized pieces off the log. Looking for good solid wood through the center. I'll do this for logs that started to rot from the center up (or down) as well.
Sometimes I'll find I've cut off a piece that will make cool bowl blanks, and that will be what is is saved for. Once I get to a place the wood looks 'solid' enough to bother using a mill, I'll mark off about 8.5' and cut the log again. with any luck it will look similar to the other end. At which point I'll try another 8.5' etc. Of course while marking the 'log' length you need to look for places large branches broke off and might be rotting into the center of the log, these can possibly ruin 2-3 feet of the log in the center.
I've done this the most with oak, and you can have soft squishy rotted wood an inch or two thick and the center can still be wonderfully firm.
One thing to look for before even cutting into it is how the log is lying on the land and the conditions it is lying in. Marshy land can ruin a log for anything but bowl blanks in a long hot summer. Dryer uplands one can last quite a bit longer and still produce some colorful boards. if the tree is 'spanning' a distance, (not touching the ground between to small lumps or a slight curve etc) then it can be good for a very long time, they tend to crack all the way to the center after a while though so they also have a limited time for wood working too, though stay good for firewood!
Depending on your time line from when you get to check the wood to when you want to process it, one test that can show you a lot, (even on 'green' trees) is to cut off a firewood sized chunk and let it dry on the driveway or in your shop. stuff that looks good and solid might look quite a bit different after drying out for a week. I've had to learn that one the hard way.