I've got about 500 hours in an E model - some notable items:
1. The overhead trim crank will drive you nuts for the first XX number of hours until you really get used to it and can trim without thinking or without trial-and-error cranking.
2. The first notch of flap will cause a big pitch change - after a number of hours you will learn to anticipate the change and make smooth control inputs to counteract it.
3. Does your Aztec have dual hydraulic pumps? If not, that royally sucks; if you lose your only pump on the wrong engine, you are left with the really crappy prospect of hand-pumping the gear up on takeoff/climbout (the planes were originally certified with one pump, on one engine, can't remember which side).
4. I agree with the nose-heavy comment, especially when you have 2 people up front, at least in the one I flew. Run some W/B loading scenarios to see what you're dealing with.
5. It's never happened to me, but I've heard second-hand incidents of the door opening up in flight (when it wasn't latched securely) and resulting control difficulty and problems holding altitude.
6. MOST IMPORTANTLY, you need to have a fuel management routine for flying this plane, especially if you are used to a simple fuel system that doesn't need tank-switching. If you are doing short hops, the fuel mangement won't be a big deal but for longer flights you will need to be doing some timing, switching tanks, and monitoring burns. If you have tip tanks, that will add a little complexity (i.e. if I remember right, the outboard fuel gauges measure the outboard tank and the tip, but only when the tip has a certain amount of fuel, and there if some fuel-ciphoning peculiarities involved between the tip and the main tank, too...it's all in the AFM supplement so it's good to review this carefully if your plane is so equpped). Don't forget that the center position on the fuel selector is OFF!
My setup for fuel management was this: I kept two count-up digital timers on the yoke, one for the outboards and one for the inboards. I would start and stop the applicable timer depending on what tank I was using, thereby keeping a running tab of the time used out of each tank. I think I ran on the inboards for one hour, the outboards for another hour, then back to the inboards for 30-40 minutes, then outboards for 30-40 minutes. That left me with about 45 minutes of reserve. At the height of my Aztec flying, I had exact fuel burns and timing nailed down pat.
I don't have anything to add about the Garmin 530 that hasn't been said already or that isn't common sense, except a gentle reminder: make sure that you guys know your way around the box in good VFR before trying things in actual IMC.