What is required of one who made a mistake in the Tashahhud by putting one word before another, so instead of saying "التحيات لله والصلوات والطيبات" (All greetings are for Allah, and prayers and good deeds), they said "التحيات لله والطيبات والصلوات" (All greetings are for Allah, and good deeds and prayers)?

If one makes a mistake in the Tashahhud (definition), there is nothing against him as long as he did not intentionally change the meaning. If he changed the meaning, his prayer is invalid if he did so intentionally. However, if he did not change the meaning, the madhhab (definition) (school of thought) holds that his prayer is valid. The error mentioned in the question does not change the meaning, and he only needs to correct it.