This is the pair where the wrong word is most likely to offend, and the mechanism is worth understanding. A disinterested judge is doing the job properly. An uninterested judge is asleep. Call the wrong one by the wrong name and you have not made a spelling slip — you have made an accusation.
An adjective meaning impartial, having no personal stake in the outcome.
An adjective meaning not interested, bored, indifferent.
Uninterested is the simple one: it means not interested, bored. Disinterested means something more specific and more useful: impartial, having no personal stake in the outcome. A disinterested referee is exactly what you want; an uninterested one is not.
Disinterested has been used to mean uninterested for a long time, and many people now use it that way. But careful readers, and many editors, still treat that as a mistake, and the precise meaning of disinterested has no other good single-word replacement. Using it correctly keeps that meaning available.
The test: if you mean the person doesn't care, it is uninterested. If you mean they have nothing to gain or lose, it is disinterested.
The audience seemed disinterested in the second half of the talk.
✓The audience seemed uninterested in the second half of the talk.
They were bored, not impartial: uninterested.
We need an uninterested third party to review the contract.
✓We need a disinterested third party to review the contract.
The point is someone with no stake in the outcome: disinterested.
He's completely disinterested in football.
✓He's completely uninterested in football.
Not caring about something is uninterested.
Quick way to remember
Ask whether you mean "impartial" or "bored." Impartial takes "disinterested" — think of "interest" as in a financial stake, which a disinterested person does not hold. Bored takes "uninterested." If you are describing someone's fairness, never use "uninterested."
Is disinterested ever correct for "bored"?
It is common, and some dictionaries list it. But enough readers object that uninterested is the safer choice whenever you mean not interested.
What is a good synonym for disinterested?
Impartial, neutral or unbiased. "A disinterested observer" is an impartial one.