WrightAvia's comments are right on the money!
The door can be closed with demeanor and grace. Says it all about the airplane. Learn to close the door, and fly it with the same style. Slam it around, and yes, you will close it, but......
Know "the numbers". For the later fuel injection models, 17" MP for a nice ILS. Gear and flaps do the rest. 15" on the F model/carb/underwing exhaust.
As the proud owner of an N model that met its demise in a gear up touch and go by a renter, I can second the middle detent caution. Also, I'd avoid doing a full fledged manual extension of the gear. The small helical gears in the crank handle are not sufficent for training-- ours ended up stripped. Good thing they were not needed one day, and we caught it on an annual!
Regarding Aux (electric) fuel pumps. A service bulletin, mandatory for 135 optional for 91-- Switch is labeled LOW-OFF-HIGH. As manufactured, low is low, off is off, HIGH is really low unless a pressure sensor detects low pressure. Service bulletin makes it do what it say-- low-off-high. Two ways to tell (well, 3 if you have proper logs): Service bulletin consists of cutting and capping pressure sensor line, and changing out switches. If completed IAW cessna bulletin, new switches are like a gear switch to get into high (up) position-- that is one must pull it "OUT" and "Up". Also, if a pump is running in high at idle/on ground, the engine will run like crap and/or quit. Some say that is why cessna originally tried to make it smarter than the pilot. However, as the owner of a '68, I was glad to have the SB, as a weak diaphram could mean the pump always runs in low, even in high position. If the mechanical fuel pump takes vacation, you want the aux pump putting out high.
So.... you can see the fuel system is a great way to give an applicant a run for the money on an oral. Know the systems, be confident in your answers. No matter where the fuel comes from, the excess is returned to the engine side (that drew it) main tank!
Electrical gave some students trouble-- Dual voltage regulators, and a switch labeled "Emergency Power", and another "Emergency Radio". I heard answers on that one including a spare battery! Emergency radio simply bypasses the radio master relay, and ties radio rack straight to buss bar (hence the BIG toggle instead of little one). There are two fuses for field relays-- technically to be IFR legal, you will need a spare. We had spare in a fuse holder, but renters always took it out, figuring the spot was to hold pencil!
Performance-- The airplane falls in the category requiring single engine climb of 50fpm to 5000ft (is my memory rusty on #'s?). The weight is below 6000lbs, but the stall speed is above 61 knots. So performance section is a bit more robust than some books. Ground skool will teach you not all twins have to climb on one engine! the CE310 must (at least when it was certified).
It's a great airplane. Enjoy it.