On average, there are 500 to 600 mistakes made in every 60,000 cycles of fertility treatment, according to the Human Fertilisation and Embryology Authority (HFEA).
The body's latest report suggests that, from the start of 2010 to the end of 2012, there were 1,679 adverse incidents in UK fertility clinics.
The authority, which licenses fertility clinics and centres carrying out in vitro fertilisation (IVF), other assisted conception procedures and human embryo research, said there were three of the most serious adverse events, known as grade A mistakes, during this time.
One of the most serious mistakes reported was a family receiving the wrong sperm.
The couple was supposed to be given donor sperm from a specific donor - so their child would have the same genes as their sibling - but they were given the sperm of a different donor.
HFEA said the most serious incidents occurred "infrequently", but the number of grade C mistakes - such as breaches of confidentiality or one of many eggs being rendered unusable during the processing of treatment - remains too high.
HFEA chairwoman Sally Cheshire said: "While we do what we can to ensure IVF is error free, mistakes do sometimes happen, as they do in any area of medicine.
"What's most important is learning the lessons from errors made to minimise the chance of their happening again."