Disclaimer: Clifford Evans is not responsible or liable for any actions you do or do not take as a result of reading this article.
Soundboard Look for cracks in the soundboard, wooden bridges and even the iron frame itself. Some cracks are more serious than others. Also look out for woodworm, although in my experience, it is quite rare in upright pianos but it would be enough to put me off.
Will the piano stay in tune? Ask your piano tuner to test-tune a few notes and comment the state of the wrest plank - the piece of wood which the pins are in. If this is not in good condition, then the strings won't stay in tune very long, and your tuning bill will soon mount up. If your tuner says the wrest plank is too far gone DON'T BUY THE PIANO because it is likely to cost too much to repair or will need to be tuned too often. Remember that you will need to have the piano tuned regularly - at least twice a year if not 3 or 4 with more usage.
Left pedal, una corda of your upright piano should be working properly, making the notes quieter by pushing the hammers closer to the keys and thereby reducing their striking distance. Older pianos use the method of pushing up a piece of felt between the hammers and the strings, but this is more useful as a practice pedal for not disturbing the neighbours. However some newer uprights have that facility incorporated as a middle pedal.
Right pedal of your upright piano - often called the sustaining pedal - should also be working properly, and one simple test is to depress the pedal and then play any notes on the piano, without holding them down. Now let go of the pedal, and the notes should stop sounding immediately, although on upright pianos there is often a small amount of resonance after the pedal has been released.
Piano environment Take note of the circumstances of the piano: was it kept in an environment with a fairly constant temperature and humidity, or has it suffered extreme changes? Has it been kept next to a central-heating radiator? This is very bad for pianos, especially old ones, because the water-based animal glue becomes ineffective, and you have lots of repair bills. You also need to take your tuner's advice about the environment you are putting the piano in, because if you take an old piano from a cold, damp house to a warm, centrally heated one, then this will cause the piano a lot of problems and the damage can be quite devastating.
Privacy Another factor is the number of rooms you have in your house. For an acoustic piano you ideally need a separate room for your privacy, best concentration and not to disturb other members of your family.
Moving the piano An acoustic piano can not be moved around easily so if you go away anywhere you can't stick it in the boot of your enabling you to anywhere. If you do need to move your piano into another room, be sure to use professionals, as pianos are very heavy things and need specialist equipment and experience.