In this instance there's no reason to panic. In fact, a third dose of MMR is usually given if there's a widespread outbreak of the disease itself or sometimes even when you are not sure about the child's full vaccination status.
Different countries follow their own guidelines. The MMR and varicella vaccinations should be given at the same time or separated by at least four weeks.
There's also a quadrivalent MMRV vaccine as well - combined Measles, Mumps, Rubella & Varicella (chicken-pox)
PS: The main issue here is carelessness with lack of proper attention. The hospital should first address this issue. Vaccine mix-up can happen anywhere, and normally it should only be a very rare occurrence. There should be a system in place to prevent this from happening. Usually it's a Check, Double Check and sometimes a Triple check before you administer anything.
To slip past four different instances is not tolerable at all. Safety first. Things could have been worse. Also the way they responded afterwards is not professional. It's understandable that the parents making a fuss, but that could have been handled in a better way by the management.