The person who comes to collect your car will not actually be a mechanic, They are more likely to be an agency collection/delivery driver. They will do an appraisal on the vehicle noting any damage and you will sign to say you agree to this. The finance company will then look and see if the damage on the car falls in line with what they call "fair wear and tear." They dont expect the car to be in the same condition as when you purchased it, but it should be in line with whats expected for its age and mileage.
They will expect you to have serviced and maintained the car in line with manufacturer reccommendations so you havent wasted your money getting the timing belt done. Similarly, They will expect tyres to be above legal limit and the MOT to be current.
This proceedure has been tightened up significantly as all finance companies are getting lots more cars back this way and are looking to cut costs. For example, You should expect them to query if the service book is missing or all keys are not present. If they do chase you for any extra money for rectification costs, you need to challenge them and fight your corner.
Also, If you are thinking of financing another car now, it might be prudent to arrange your finance as soon as possible as although this should not affect your credit rating, It has been known for finance companies to record something on your credit report.