Second hand cars seats can't be guaranteed to be safe or work in an accident (which is the point of them - to protect the child in the event of a car crash).
How the car seat has been used? Has it been sitting in a car for 5 years baking in the summer sun or has it been passed around a family?,
How has it been stored? Storing in a garage or attic with high temp fluctuations which cause plastic to degrade faster,
Has it been dropped? Dropping a seat can break it or cause hairline fractures which weaken the seat,
Has it been in an accident? Child car seats are one time only items - once they have been in a crash they are junk - they have served their purpose and need to be replaced,
Has the seat been recalled by the manufacturer due to safety issues?
Are the straps frayed? As frayed straps are weaker than non-frayed one and indicate heavy usage,
Is any part of it broken? Look under the covers and check the polystyrene,
Are there any stress marks in the plastic? As white or paler than the original plastic marks indicate the plastic is degrading and the structural integrity is breaking down this means the seat is definitely not usable,
Have the straps been immersed in water to clean them? This removes the flame retardant - if the situation is so dire you need the straps to be flame retardant you really need for them to actually be flame retardant!,
Are the instructions included? If they aren't how will you know you are using the seat properly?
Does it meet current safety regs.? ECE R44/04 or ECE R44/03 (03 is the older standard as 04 came in, in 2005). Anything earlier than that or with a Kitemark are illegal and incredibly unsafe now.
Do you trust the seller with your child's life as you are trusting them not to sell you a seat that has been in an accident or dropped down a flight of concrete stairs....
These are all questions you need to ask (either of the seller or of yourself). Wouldn't it be easier just to buy a new seat? Even if you get the answers to all the questions there is still no guarantee the seat is safe. The only way to tell if a car seat will perform in an accident is to crash it on a test sled in a lab and then it isn't safe as it's been crashed....
If you genuinely can't afford to get a new car seat (and while the £30 car seats aren't great they do meet the minimums [which are very crappy to be honest] and they won't have been in an accident or had bits broken off them) the hospital may lend out car seats to those in financial need to get home from hospital safely.