I'll go about this from a syntactic point of view using phrase structure rules.
The structure of a noun phrase in English is:
NounPhrase -> (Determiner) (Adjective +) Noun (PrepositionalPhrase +)
(How English Works; Curzan 175)
Determiner: Words like "the", "a", etc.
Adjective: Words like "late", "great", "strong", etc.
Noun: Words like "car", "computer", plural forms, possessive forms, proper nouns (names) such as "Michael Jackson", etc.
PrepositionalPhrase: Phrases that start with a preposition (e.g. "at", "in", etc.), and are followed by a
NounPhrase, e.g. "at the beach", "in the house", etc.
The notation of
( ITEM ) means that ITEM is optional, and not required to form the NounPhrase. The notation of
ITEM + means that there can be 1 or more of ITEM (e.g. "the strong, courageous woman").
So, here's how The late Michael Jackson’s parses:
Determiner Adjective ProperNounPlural
If we look at our
NounPhrase rule, this part of the sentence exactly conforms!
So, syntactically, this is absolutely correct, because determiners can precede nouns in a noun phrase.
As you have noted, it seems incorrect to use a determiner before a possessive noun, but the adjective is what compliments the determiner.
There are more complicated phrase structure rules, but even from the basics we can see that syntactically, the sentence is valid. However, we also note that the adjective is used to compliment the determiner when used before a possessive noun, and is just another quirk of English!
Edit: You may also be interested in using the Stanford Sentence Parser in order to get a sense of what each word functions as, and what its place is in a sentence.