As I understand it, within well-known limitations, facial reconstructions can be very accurate. There have been several instances where recent unidentified remains have had the face reconstructed as an aid to idenditifcation, which subsequently when the identity of the remains has become known, have been very close to photos of the deceased. There will always be some features that cannot be reconstructed simply from skeletal remains, such as hairstyle, body decorations, fleshy wounds and scars, and the overall degree of body fat/fleshiness, but even these can sometimes be inferred by circumstantial evidence: in archaelogical terms a high status burial of a middle-aged adult is likely to have had a well fed and fleshier face than that of a young adult agricultural worker in a common grave.
How important any errors or uncertainties in the reconstruction might be also rather depends on why one is doing the reconstruction. Reconstructions of the faces of a historical persons, such as Tutankhamun, Richard III or Ivan the Terrible, obviously aim to get as close to what they actually looked like 'in the flesh'. However accuracy is rather less important in the case of your example of Cheddar Man, where the reconstruction is to show what people of his type looked like, and in particular in that example to emphasise the striking fact (obtained by DNA analysis) that he had dark hair, dark skin and blue eyes. Similarly the facial reconstructions of several of the crew that were found on the Mary Rose (sunk in in 1545) are in themselves not particularly valuable, revealing the men concerned to have fairly unremarkable faces. Of more interest were the hidden physical aspects of the bodies: for example from memory the gunner on the Mary Rose had healed lower leg injuries commensurate with a accident while manhandling heavy cannon, while the cook had an old debilitating back injury, hence why he was the cook and no longer an active deck-hand.
Nevertheless for all the 'Madame Tussauds' aspect of these reconstructions, they do inevitably serve to demonstrate that such historical people, the well-known or anonymous alike, still looked very much like ourselves. In that regard the facial reconstructions of near humans, such as neanderthals and even older hominids, is valuable in showing people who, while not exaclty like ourselves, would still likely have been able to blend in reasonably well on the London Underground if only given a shave, a haircut, a suit and a mobile phone to stare at. And that is surely a valuable lesson in humility and in better understanding our place in the history of the world.
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