Look at the Cassette and Chainring Teeth

Worn teeth confirm what the chain checker suggests. Healthy teeth are evenly shaped; worn ones turn hooked and pointed into a shark-fin profile as the chain eats into one face. Check the cogs that get ridden most, and the chainring teeth all the way around. Watch for a shiny new chain running over hooked teeth. It can mean the seller replaced the cheap part and left you the expensive one, and a new chain on badly worn sprockets is likely to skip, especially on the smaller cogs, which hard pedaling on the test ride will reveal.