At this web site
Kester gives a test for whether solder paste is fresh enough. The test is to melt a drop of it onto an unsolderable surface and see whether it forms one ball or several. If it sheds a number of smaller balls (rather than forming just one), the flux has deteriorated. The failure mode is flux deterioration.
The funny thing is, I have some solder paste that is 10 years old and seems to pass this test. I'm going to repeat the test more rigorously.
Presumably, paste that is too old for surface mount work could still come in handy in larger-scale work. It's still solder, after all.