The fundamental mixing decision in jazz is how much compression to apply, and the answer is "as little as possible." Modern pop mixes might have 5-8dB of constant compression on every element; a great jazz mix might have 1-2dB on a few tracks and zero on most. The dynamic contour of the performance — the way the soloist gets quieter during a tender passage and louder during a climactic phrase — is the entire emotional content. Compressing it crushes the music.
The stage layout is built into the panning. A piano trio recorded live in a club has the piano on one side, the upright bass center-back, and the drums center-front. The mix should reproduce that. Each instrument gets a specific pan position that places it in the listener's spatial map. Done right, a jazz mix on headphones gives you the sensation of sitting in the front row of a small club — every musician has a location, and the spatial coherence sells the realism.
Room sound is more important in jazz than in any other popular genre. The decay characteristics of a real room (concert hall, jazz club, or studio with the right acoustics) blend the players together and provide the "we're all in here together" feel. The room mics are typically mixed at -6 to -3dB relative to the close mics — substantially louder than rock or pop would tolerate. If you don't have great room mics, a convolution reverb modeling a small jazz club (Avatar Studios, Sear Sound, etc.) is the next-best option.