Signs of a dying cpu are that it starts to make more mistakes.
A bit flip here. Some corrupted cache there.
The symptoms can range from blue screens of death to the occasional retransmit of a network frame or miscolored pixel. Basically everything has bit that could fail, and the function will determine the severity of the symptoms.
To make matters worse, this is also the same behavior when the power supply is unstable, the clocks are too fast, or its running too hot.
The symptoms are most often linked to bad memory, which is more likely to suffer from problems due to being on a separate board, build to a price and often lacks self correcting mechanisms. (ECC)
In short: the end user can't determine it. You'll need in depth knowledge of the architecture and test methods used to test silicon. A complete test might not even be possible anymore once it has been packaged. (Eg: put on little board with heat-spreader)
Anyway, please let me know when you've worn out a silicon chip by using it inside specifications. The bathtub curve rising section is many years away from the point it becomes obsolete and slow.