Quarantine is only effective as a PHYSICAL barrier to disease, e.g. isolation, destroying infected items. This is a disadvantage as many diseases, like avian influenza for example, can be spread by wild birds that naturally migrate over borders. It is exceedingly difficult stop this kind of spread without culling - something which is detrimental to the environment as it decreases biodiversity.
Also, with globalisation there has come a breakdown of the barriers of time and space, e.g. airtravel, so diseases are able to spread quickly and often undetected for this reason. Take swine flu as another point in case.