Here are just a few of the items to watch out for.

1. Make sure you SLOW down! 10Mph MAX
2. Turn your lights on when inside one even if they are well lit, it will make you more visible.
3. If the car park is barriered then ensure you get close enough to the ticket machine to be able to reach the ticket issue button.
There's nothing more embarrassing than either having to get out of the car to get your ticket, or your backside high in the air whilst you are leaning out of the window trying to reach the ticket machine.
Trust me, your mates will have a good laugh at you.
4. Ensure you don't hit the ticket machine, or stop too late and take out the barrier.
5. There are LOTS of concrete pillars holding up each level, (although the more modern Multi-Storey car parks tend to have smaller pillar)s if your car hits one of these you'll do more damage to your car than you will to the pillars. So keep slow and watch out for how fast or slow you turn the steering.
6. Pedestrians can appear from anywhere (especially children) watch out for them!
7. Drivers with lack of awareness may reverse or drive out of bays without looking first.
8. Ensure you have enough money to pay for your ticket and don't dawdle back to your car once you have paid (if this is the style of payment required), you only get a certain amount of time to leave before you will be charged more if you are close to the time limit you have paid for.
9. A lot of Car parks are now installing ANPR
(Automatic Number Plate Recognition systems).
These machines issue the ticket to your vehicles number plate.
There will also be an ANPR camera at the exit and will recognise your vehicle when you come to leave so "should" open the barrier automatically.
If it is night time your lights may blind the camera and it will not recognise your number plate so the barrier may not open.
This is an easy fix, turn your lights off, give the camera a couple of seconds to read your number plate, If it still does not recognise your car, feed your ticket back into the machine.
10. Watch out for time of use signs. Some Multi-Storey car parks are locked up at night to avoid vandalism, homeless people sleeping in them or drug users using them during the night.
11. Pay attention to what floor and row you have [parked you car on before leaving to go shopping etc, not remembering where you are on your return could make the difference of an extra hours charge on the meter if you go over time.