One of the main things about Hal was his teaching of listening to what was going on around you as you played. Listen first and play second was his big thing. The more you're listening to those around you, the better you can react to what's going on. This, of course, means the more control you have over your instrument the less you have to be thinking about the technical aspect of music. This clears your head out to be able to just listen to, and react to what's going on in the group of musicians you're interacting with.
Something that was vital for me in his teaching was his ability to tell you that you sucked. Not to dress it up, rose tint it, and tell you you're amazing even when you're having a crap day. He would tell it like it is, and not beat about the bush. Getting right to the point and focusing on what to do to get better at things you were weak at. Like any good teacher one of his main things was time as well as listening. In a culture of improvised, jazz bass music, rhythm is such a huge part of that, and is something that gets hugely overlooked. We would develope tunes, melodies, phrases and play all kinds of things using rhythmic constraints to force us to focus on certain aspects of rhythm that we might not have be aware of before.
Playing a solo on a song at 200bpm and using nothing but half time triplets as the rhymic basis for the solo......... this will make you find different ways of making tension and release, and shape your solos in ways you might not be used to. Basically, anything you can do that helps you find something that you never played before is great.
Easy,
Janek