There will be many who bought privately and got a good deal with no problems. But equally there will be not an insignificant number who have had a poor experience when buying privately. So what your really asking is "how do you spot a bad deal.
Sadly there are an increasing number of scams out there, and the scammers are becoming more adept at covering the tell tale things that can give the game away. So you have to be very aware, and if anything seems even just slightly odd be prepared to walk away. You must use your head not your heart.
With private sales, it's much much harder to protect yourself if anything does go wrong, there are no guarantees and that is one reason why using a dealer can be worth while as you automatically receive the full protection of the Consumer Rights Act 2015.
You must ensure whoever is trying to sell actually has the right to sell it, does the documentation match the caravan, and the name and address of the person selling, is there any outstanding finance on the caravan. Look to see if the seller has more than one caravan to sell, if they do, he is legally a trader and may be selling privately illegally to off load a lemon.
A full service history can be an indicator of how well a caravan has been looked after, but it does not guarantee the caravan is in good condition, check for any signs of damp. Go prepared with a list of questions, for example "Has the caravan had any history of damp problems" make up other similar questions that encourage the seller to tell all.
If after seeing the caravan it looks promising, do not make an offer before asking if the seller would mind you having an Approved Workshop Scheme engineer do a full check on the caravan before you agree to buy it.
If you meet with any resistance to the questions or the suggestion of having an inspection. Ask yourself what are they trying to hide and walk away.
If you have a friend or family member who is a seasoned caravanners, ask them to come and look at the caravan with you. They may spot something you might miss