Bigband player here.
As for intonation, I try to set myself so that I would be able to 1) hear myself 2) hear the piano 3) hear even the farthest and most silent woods. I'm listening to everything, piano being more important than other instruments as it cannot change tune. Notice I don't mention guitar - I found out that I'm not able to hear guitar's intonation very well, due to rather deep and bassy tone usually used usually swing comping. Generally, I think that horns and voices should be intonating according to bass and not vice versa, so I try to supply authoritative and precise intonation.
As for rhythm, I listen to and strive to be in precise timing with: 1) drums 2) myself 3) guitar 4) everything else. Generally in that hierarchy. I feel that the 'rhythmic authority' of rhythm section is shared mostly between drums and bass, one driving the other, and the other driving the first; the rest of the band reacts to drum+bass rhythm.
That's my theory which I really never discussed with anyone. In practise, most intentions come out less brilliant than intended, and of course other instruments have theories of their own. The most important method to 'make us sound better' I know of is to look for more and more subtle rules and sort them into some kind of hierarchy.