Answer:
The biggest weakness is that it was not legally binding. Countries signed the compromise, but they were not obliged to meet the criteria. This is a big reason why it was replaced (not officially replaced, but replaced in fact) by the Paris Accords.
Another big weakness of the Copenhagen Accord is that it was signed by only five countries: the United States, and the BRIC countries (Brazil, Russia, India and China). These are five huge countries that represent a great share of the world's emissions, but they still do not include big emitters like Germany or France.