We've had a moses basket bought for us (I know it came from a charity shop but other than that don't know it's origins) and have read that you should always get a new mattress is you use a second hand cot/moses basket. However, the mattress in the basket is a waterproof one ie; totally wrapped in a waterproof material and sealed up.
If the mattress was just like a normal foam mattress that couldn't be cleaned properly I could understand the need to buy a new one, but surely just disinfecting this one should be enough, shouldn't it?