Just a couple of brief thoughts here.
That C# fully diminished seventh chord I have always heard as a secondary leading tone chord. Yes, I know, it can be thought of as having a secondary dominant function and I agree with Ethan about that. The flavor, though, is secondary leading tone chord. The C# fully diminished seventh chord rising to the D7 with the split third F natural up top sounds right, and the reason I hear the C# as just that is I sat down and played through that C# dim 7 chord as if it were a standard secondary dominant chain A7 to D7#9 and it just sounded all wrong. From a linear and contrapuntal standpoint the C# secondary leading tone chord is the right call. I know theorists may differ but that's my conviction. Building a secondary leading tone chord on an augmented fourth is still bluesy. Ethan's discussed the use of diminished seventh chords in blues in the past and I had a response post highlighting a spectacular passage from Villa-Lobos planing fully diminished seventh chord shape down the entire guitar neck. You can go look that up if you like.
So first thought is about the secondary leading tone chord that's a fully diminished seventh chord.
That G to A flat modulating reminds me of Stevie Wonder at two different levels. The semi-tone modulation resembles "Living for the City", which I have long considered "Man in the Mirror" to be a spiritual counterpart for. Stevie Wonder's song is about the desire to change the city (and I can't resist throwing in references to the Christian anarchist Jacques Ellul's
The Meaning of the City because I am a bit of a fan of him). I think of the final chord in Stevie Wonder's song as the grand unresolved neapolitan substitution in a never-resolved plagal cadence. It's the "Amen" to a Gospel song where the IV chord is never allowed to reach the I because this song is about what we have now, not an eschatological end to toil and suffering that shows up in the major prophets of the Hebrew Bible (Isaiah, obviously).
"Man in the Mirror" has a modulation up a semitone but then there's that sprawling D flat. Ethan Hein hears it as if we've modulated into D flat major with a lydian element. I have always, and I do mean always, heard the song as ending with a spectacularly long unresolved plagal cadence. The reason I hear it that way is because of how long he band hammers the key of A flat with chorus right up to that D flat chord. There's a whole minute of cycling through choruses in A flat, replete with dominant prolongation passages. When the D flat chord hits at 3:51 it's obviously the IV chord after so many V-I resolutions in A flat major. That harmonic memory doesn't go away for Michael or the band, as I hear it. If you are sticking for a long time on a subdominant chord but keeping the music strictly diatonic then lydian would be the literally natural sonorous implication of staying on the subdominant. Lydian is an asymmetric scale and the inversion of phrygian, the augmented fourth can suggest a secondary leading tone to the fifth of the scale but in this case the augmented fourth on a subdominant chord is just the leading tone of the key. I mean, at the risk of noticing Crouch did the choral arranging, when there are so many obvious nods to Gospel I think that's an extramusical but still musical indication that a giant unresolved plagal cadence is the best way to understand the song "Man in the Mirror".
The song would lose its emotional potency if you ever actually resolved that D flat chord to A flat, and it would become comical if the D flat went to E flat and then to A flat but cycling through the usual I, IV and V via secondary leading tone chords previously mentioned is what we've had going on through the song until this closing D flat major chord. It's not that the song has exactly modulated to D flat so much as that the various harmonic prolongations that have shown up earlier in the song and the lyrics cement an idea that a change has to be made but the change has to come from you and me as Michael is singing to us, for us, and for himself performing the song.
I didn't particularly like Bad when it came out and it was the beginning of the end of my fondness for Michael Jackson's music but this song was one of the best songs on the album and it still works decades later. It sure holds up better after all these years for me than "Speed Demon" or "Dirty Diana". I'm not saying you can't like the album, just reminiscing about feeling disappointed and underwhelmed by the album when it came out. It still had good songs but it did come after Thriller. I'm reminded of something I said to a friend about a movie I won't name that was a sequel, which is "Bitterly disappointing is not the same as actually bad."
But I digress. I think "Man in the Mirror" ends with a gloriously unresolved plagal cadence and that it takes up thematic and musical elements I hear in "Living for the City" to similar effect.
So for me there is only one modulation in "Man in the Mirror" but theorists can (and should) debate this point. The song's use of harmonic rhythm and phrasing is why, though that's based on what my ears tell me as I don't actually have a score for this one. I used to sing in choirs in college and at church and maybe I should concede that if you have done enough singing in church you can (or may) hear things like the end of "Man in the Mirror" as not having a modulation because of performance experience. I can see how that D flat could be heard as established as a new kind of tonal center and I don't really dispute that, I just hear it differently because of my background as a classical guitarist and volunteer church musician who also has some background in choral music.
It's as necessary for "Man in the Mirror" to never reach its tonic as it is for "Living for the City" to not reach its tonic at the end for is musical and lyrical point to be made. Somewhere, somehow I heard a version of Stevie Wonder's song where that neapolitan chord resolved down to its expected tonic ending and it felt weirdly tossed off an anticlimactic. After all that came before in the song to actually reach the tonic after such a dramatic subdominant prolongation becomes a musical and lyrical bad joke that says, "Well, yeah, everything's magically better now and nobody actually needs to change at all."
Never-resolving chords happen in classical music, too. An example of an unresolved half cadence (which I actually
hate) is Virgil Thomson's arrangement for chorus and piano of "
How Firm a Foundation". One of the most memorable examples from my own choral singing background is that gorgeous unresolved F sharp dominant seventh with an added 9th (which I love) is at the end of Durufle's
Requiem. There the unresolved dominant ninth chord obviously symbolizes the never ending rest of Heavenly bliss from Requiem mass. Unresolved chords can have all kinds of text-painting functions in vocal music and some of the most memorable and riveting endings in pieces of choral or vocal performance come when the "end" is deliberately impossible to resolve for the sake of expressing a point made in the text of the song, whether it's Durufle's "
in Paradisum"; "
Living for the City", "
Man in the Mirror". When you know what textual point you want to make in your music then there are times when the where, when, how, what, and why of breaking every harmonic "rule" in songcraft dictates that you break allegedly sacrosanct harmonic rules to respect the point of what the words are saying is the point of your song.
Ergo, the massive unresolved plagal cadence in "Man in the Mirror", as I've been saying through the whole post.