No fertility clinic who has gone through such a horror would shout this fact from the roof tops. Nobody wants to scare off potential clients, and fertility clinics are no different to other companies in that they would probably rather hide their mistakes from the general public. However, if you ask direct questions, you should get the information you need. What if you find out that the clinic you were considering for IVF has had embryo mix-ups in the past? Should that automatically disqualify them from your selection process? No, I think, but you should find out in great detail what happened and what your fertility clinic is doing to ensure that such tragedies will not take place in the future.
A past embryo mix-up should make you very cautious, but fertility experts rightfully point out that, where there are humans, there is room for human error. A quick look into what happened at past embryo mix-ups reveals that improper labeling of embryos, or two clients with similar family names, are usually a part of the error. Ask your fertility clinic whether they use electronic tracking using unique radiofrequency tags. Such systems have been introduced recently in the United Kingdom with great success. When an embryo is taken to the wrong place, alarms physically start ringing.