I'll focus on the end, which is where the tune deviates from a normal blues.
Harmonically, the bass is ascending chromatically from B, while the chords descend chromatically from E♭Maj. (You can most clearly hear these chords in the saxophone, which outlines those triads in the melody.) The combination of ascending and descending creates an interesting contrast, and it results in some weird chords: E♭Maj/B, DMaj/C, and D♭Maj/D.
Rhythmically, it's equally strange. Things start to get weird in measure 9: the melodic phrase from the end of measure 9 feels like it begins one beat too late. This is no coincidence; a nearly identical phrase occurs in measure 4, starting on beat 2. But when we hear this phrase again in measure 9, it starts on beat 3 (one beat later), and it doesn't conclude until beat 2 of the following measure. As a result, it feels like the downbeat of measure 10 is delayed from beat 1 to beat 2. The rest of the band emphasizes this staggered feeling by playing hits on beats 2 and 4 of measures 10, 11, and 12, which further makes the listener feel like the downbeat has been delayed from beat 1 to beat 2.
On the solos, there's a different form for the bass than for the rest of the band. Generally, each measure of the melody has been doubled for the solos. But the bass solo is only 22 measures long, whereas the other solos are 26 measures long (double the head). The bass solo deviates quite a bit from the harmonic structure of the head, but the other solos do too.
None of the solos include the strange descending/ascending chords featured in the melody, but the pianist does repeatedly use a chord substitution in the last four bars, which goes something like | E♭7 | A♭7 | G7 | C7 |. You can tell it's a substitution and not written into the sheet music because, at 1:56, the bass is riffing on the F7 lick while the pianist's left hand is playing the chord substitutions. Something similar happens at 2:24, the second time through the form on the pianist's solo. The bass riffs on F7 and doesn't pick up the pianist's chord substitution until G7. Overall, though, those substitutions most likely weren't part of the written music. I think the chords written for the solos were pretty simple.
Here's everything I'm hearing. Measure 13 of the head is one octave lower.