The number of mistakes at IVF centres in England and Wales rose from 182 in 2007/8 to 334 in 2008/9.
Blunders included embryos being lost or implanted in the wrong woman, and eggs being fertilised with another man's sperm.
The figures from Human Fertilisation and Embryology (HFEA), the IVF regulatory body, were obtained by BBC Radio Five Live's Donal MacIntyre show.
The HFEA said the errors represented less than 1 per cent of more than 50,000 IVF cycles carried out.
One couple were told by the University Hospital of Wales's IVF clinic that their last remaining embryos had been lost during treatment.
The pair, identified only as Clare and Gareth, had been trying for a baby for eight years.
Clare told the BBC: ''I was sat there, gowned up, waiting to go in and have a transfer. They said you've got one embryo remaining, the other two embryos have gone missing.
''They said in the next sentence I can assure you they haven't gone into anyone else. Those were two potential babies.''
The centre in Cardiff was responsible for another serious mix-up three years ago when a couple's last viable embryo was placed in the wrong woman. An investigation found serious failings at the clinic.
The clinic said its success rate in recovering embryos is among the highest in the world and all incidents are reported to the HFEA.
Clare and Gareth's solicitor, Guy Forster, of law firm Irwin Mitchell, said he has dealt with a dozen couples involved in similar incidents at different clinics around the country in the past 12 months.
He said: ''It may be perhaps that the embryos have been lost, or in the worst case scenario an embryo has been transferred into the wrong patient. It's deeply disturbing.''
Dr Sammy Lee, a fertility expert at University College Hospital, said: ''The key failure of the HFEA is that when they ask clinics to put in special procedures, they're not enforcing them.
''There's no point simply putting a request in writing and then expecting everything to be all right. You need to make sure that when you require something, that you have a way of enforcing it.''