The hand-over of a car is basically a nice conclusion of the purchase process. The car is polished, the paperwork is handled by the dealer, and the only thing on your mind is to drive off. However, it is recommended to go through the agreement you made with the seller one more time. Make sure that all the promises are honoured. It is always easier to get things done while you still have your money in your pocket.
The tyres of a car are in plain view and therefore easy to check. In order to find out if the tyres are still in good shape, you need to check each tyre individually. Start by measuring the depth of the tread, this will give you good idea of the lifespan. Because a tyre needs a minimum of 1/16th of an inch (or 1.6 mm) tread depth for MOT approval.
The quality of a gearbox depends highly on the previous owner(s). This means that you can find out what the general condition of a car is by just checking the gearbox. A poorly functioning gearbox can very well mean that the car in general has been treated badly. An important part which you should check in combination with the gearbox is the clutch.