Random stuff, but here we go. Some of these apply to only certain countries, some are advisories, and some are just common sense.
You need a high vis vest for every car occupant, and they must be in the car, not the boot. This is so you can put the vest on before getting out of the car.
Speed camera detectors are not allowed. Sat navs are okay as long as they don't actively report speed cameras.
Check your insurance covers you for all countries you're going to visit, and check it's full comprehensive cover and will apply for the length of your journey. Some insurers only allow 2 weeks at one stretch.
Carry your passport, insurance documents, MOT and V5 document with you in the car.
2 (two) warning triangles are required.
Make sure you take the spare car key, spare wheel (legal and blown up to the correct pressure), a foot pump or compressor (and possibly a tin of tyreweld for an emergency), fire extinguisher, spare bulb kit, first aid kit, locking wheel bolt key, a proper jack, screenwash, ltr of oil, etc. While you're travelling, put the spare wheel and jack close to the top of the luggage then you don't have to unload the whole boot to get to it in an emergency.
Look at getting European recovery / roadside assistance. It costs as little as £60 for full UK and full European cover for a year, so daft not to.
Scan all important documents and email them to a Gmail or Hotmail account so you can download / print copies if you lose them at any point.
When driving on the right you're gonna have to rely on your passenger for a view of the road in certain circumstances. Before setting off make sure that you're both aware of what's needed in any given situation, and develop a system where you both communicate clearly. We have a code where if I say "Mirror" then the wife knows I need to see the passenger door mirror and stays out of the way. It's very easy for the passenger to lean forward and block your view at just the wrong moment!
Headlights (or DRLs) are mandatory in some countries, and make sure you fit beam benders at the port so you don't dazzle others.
GB sticker (or badge on the number plate) is mandatory. Note GB or the EU symbol are the only ones which are legal, The white ENG badge is not (I think!).
There'll be more but that'll do you for a start.