Just give it a tug. If it doesn't pull apart, then it's fine to use. I have lots of very old (think 75 to 100 years old) thread that I use frequently for my wall hangings. Sometimes the first couple of layers on the outside have weakened due to sun exposure etc., but usually if you pull that off then what is underneath was protected and is good. That said, I would throw away any that has mildew or mold on it.
I would not use some of my older threads for quilts that will be used like lap quilts or bed quilts, but I have used lots of thread from the 60s and 70s in quilts that get use as well as in potholders, and they have held up just fine.
Rob