Errors in security procedures: There are a number of instances of actions that would seriously violate security in the sequences at CIA HQ, the most glaring of which is Esther Drummond receiving a call on her personal cell phone from inside a secure area, which would never be allowed.
Much is made of the lack of deaths causing an imminent and seemingly unavoidable population explosion but the global death rate is only about 40% of the birth rate anyway. The world is already experiencing a huge and unsustainable growth in population. If there were no deaths the problem would be worse in the long run but it wouldn't be an instant disaster.
Birth rate: 19.86 births/1,000 population (2010 est.).
Death rate: 8.37 deaths/1,000 population (2010 est.).
The goof item below may give away important plot points.
When Esther Drummond is making her escape, the security guard monitoring access says that she swiped an ID card to exit the main secure area, and a second time to access the elevator. However, in a previous scene, she simply presses a button to call the elevator and simply step in.