Everything must be spelled correctly.
Or:
Everything must be spelt correctly.
Both spelled and spelt are correct forms of the past participle of the verb "to spell".
BTW I am English and use the word "correctly" rather than "correct".
It may be differnt if you are American.
Both are correct but I always say spelt. When I was writing girocheques and made a mistake I had to score through it to cancel them. I wrote "SPOILT" across them and was telt that was wrong because it should have been "SPOILED". Needless to say I ignored them and carried on writing "SPOILT".
I thought that spelled was the past tense of the verb ' to spell.' " I have spelled words correctly in the past." The word 'spelt' refers to the object ie that which has been 'spelt.' "This word has been incorrectly spelt."