Having actually read the studies that led to the headlines about sleeping on your back in the third trimester (have you read these @Mousefunky?) I'm unconvinced that the risk is so great that extremely uncomfortable pregnant women should be terrified of sleeping on their backs in order to get a decent nights sleep.
A historical study relied on asking a small sample of women who had experienced a stillbirth what position they slept in the night before they gave birth. Could you 100% accurately tell a researcher what position you slept in last night? what about if you had just given birth and experienced a traumatic loss? How sure would you be that you had slept in your back, and for how long?
A more recent study that made headlines last year found that lying on your back throughout the night sometimes caused the baby to go into 'distress' in some cases, the distress was essentially measured by evidence of a a raised heartbeat.
The researchers quite cautiously concluded from this that sleeping position may be one factor in stillbirth as they could see that sleeping position did influence the babies behaviour in the womb. Every single baby involved in that study was born healthy regardless of the mother's sleeping position in the third trimester.
There is also some evidence that sleeping on your back whilst pregnant can impact generally on blood supply round the body. As far as I'm aware it's fairly widely accepted now that you would start to feel uncomfortable (tingling toes, shortness of breath etc) and naturally change position long before this had any devastating impact on the baby.
The word dodgy was unfair, particularly in relation to the second study, but the conclusions that have come out of that research certainly aren't as cut and dried as 'sleeping on your back whilst pregnant is inherently dangerous'.
There's regularly posts on mumsnet from pregnant women in the first and second trimesters struggling to sleep because of the don't sleep on your back message and it's really unhelpful for it to continually be perpetuated without scrutiny.