+1 , finance is crucial check on many cars.
Also, the zoning in on the importance of checking the oil, but no equal attention is directed in checking the coolant levels and if oil/sluge is in the expansion bottle indicating headgasket failure.
No mention on how to check for the impending failure of a dual mass flywheel, very important in near all diesel cars and van models, and a real cuase as to why cars come to market because the vendor knows that replacemnt of these expensive components is in the post, and wants rid before it goes BANG.
Also, no mention of checking brake discs for scoring/lips, so easily done with finger access in between alloy wheel spokes.
Also, checking the chassis/vin no against documentation.