The errors have prompted the resignation of senior obstetrician and gynaecologist Janet Evans, who has led the unit since 2002, and its head embryologist, Belgian scientist Martine Nijs, who has written to the chief executive of Cardiff and Vale University Health Board outlining her concerns over safety at the centre.
The scandal came to light after a damning report into the incident was published by the fertility regulator, the Human Fertilisation and Embryology Authority (HFEA), which said there was "significant concern" over the extent of the error at the clinic.
The report revealed the mistakes were made by a specialist in male fertility who had been transferring sperm samples from cancer patients and sperm donors from two older storage containers into a new, single unit.
All of the samples were originally placed in storage before 2007 and some may date back to 1998. Frozen sperm samples can still be used in fertility treatment despite, as in this case, being over ten years old.
The unnamed worker found a number of unlabelled and broken vials in the older containers and, unable to identify who they belonged to, discarded them, without the presence of a witness and without immediately informing bosses at the centre.
His actions go against the HFEA's strict Code of Practice, which requires all such procedures to be witnessed to prevent errors.
The report revealed the specialist, who has been suspended as a result of the incident, had previously complained about his heavy workload and did not have the assistance of other members of staff.
In a second incident just weeks later, which is also described in the report, donor sperm was given to women having fertility treatment before the results of tests for HIV and other sexually transmitted diseases were available.
It is routine to screen sperm donors for the viruses when they give their first donation, but it is also compulsory to test them again six months later before their sperm can be used in treatments in order to identify infections which can take some time to develop.
Six patients being treated at IVF Wales were given samples before the screening results were known, although they were later found to be negative.
Three other donor samples were released before the mandatory six- month quarantine period was over and before tests for gonorrhoea and chlamydia had been carried out. The report found sperm samples released from quarantine were being stored alongside those still in quarantine.
Both incidents have emerged despite the regulator warning the clinic to tighten up its protocol to minimise the chances of making mistakes after a serious error in 2009.
In that case a couple from Bridgend, Deborah Hole and Paul Thomas, were robbed of their chance to have more children after their last usable embryo was implanted into the wrong woman. The woman later aborted the embryo after learning of the mix-up. Even then, the HFEA found vital safety checks were not being carried out at the clinic and overworked staff were being placed under too much pressure to clear a backlog of cases.
Mr Thomas said: "After our case they told us it was never going to happen again. They did not learn their lesson."
Jonathan Evans, Conservative MP for Cardiff North, said he had "major concerns" about failings at the unit and was urgently seeking a meeting with the chief executive of Cardiff Health Board, which runs IVF Wales.
Mr Evans said: "I'm extremely concerned about the impact on families affected by this terrible incident. It is clearly a matter of major concern that a clinic which has previously failed its patients has done so again within a short space of time."
The clinic, which has been licensed by the HFEA since 1992, had taken steps to reduce the workload for staff following the 2009 incident.
The latest report reveals that during the six months before February 2011, the centre's success rates dropped "considerably" at the same time as there was an increase in the number of cases.
HFEA inspectors said this "placed stress" on the centre especially because it came alongside staff shortages.
The HFEA has asked the clinic to limit the number of IVF cycles it carries out and to stop recruiting sperm donors until it has made appropriate changes.
However, it has stopped short of suspending the clinic's licence.
Another couple, who wish to remain anonymous but who are known to The Mail on Sunday as Chris and Lorraine, have revealed staff at IVF Wales dropped on the floor ten eggs they were relying on for fertility treatment.
Care worker Lorraine, 33, from Barry, South Wales, was told her own eggs were not viable but was delighted when her sister Diane volunteered to be a donor. Chris, 35, also a care worker, said: "Later that day we had a phone call to say the eggs had been destroyed because of a mechanical error."
"We later found out someone had been transferring them in a single container and they had been knocked to the floor. We've never had an apology."
Guy Forster, solicitor at Irwin Mitchell who has represented couples in cases involving IVF Wales, said he had repeatedly raised concerns about the unit.
Mr Forster said: "Sadly, these latest findings further suggest that little action is being taken to ensure lessons are being learnt from these devastating and wholly avoidable errors."
Martine Nijs could not be contacted for comment. Mrs Janet Evans, who is still working as a fertility consultant at Cardiff and Vale University Health Board outside the IVF unit, declined to comment.
A spokesman for the HFEA said both incidents were investigated immediately and that the clinic had been told to reduce the number of IVF cycles it carries out.
In September, Jan Williams, the chief executive of Cardiff and Vale University Health Board, warned of "grave" financial pressures across the organisation and said it needed to save £90 million in the next year.
Medical director Dr Graham Shortland said: "The systems used to store sperm have at all times been consistent with the relevant codes of practice and this has been confirmed by the HFEA in their report.
"IVF Wales has learned lessons from this experience and continues to work closely with the regulators to ensure ongoing improvement to systems and processes, in line with an agreed action plan."
A Department of Health spokesperson said: "IVF is strictly regulated in this country. The HFEA has powers to maintain patient safety and we expect them to take tough action if needed."
-The Mail on Sunday