My checklist for used cars:

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Condition:
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Check saftey belts for fraying

Undercariage
frame checkup
cv boots
tire bubbles

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Body
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Bolts Check
Overspray
Even panels

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Drive test:
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Tight radius rt
noises?

Tight radius left
noises?

Brakes
straight line check
pulsating check

Engine
Smoke out of tail pipe
spark plugs condition
compression test with 5% of each other
no engine codes set, must not be in learning mode

Highway speeds
noises
steering wobble

Idle
shuttering
rpm
smooth

Trans:
smooth shifts

Airbags
No srs lamp on

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misc
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recall completion