When Igor (the big armor) is shown for the first time in the movie, the suit heads over to one of the crane's legs and stays under it to keep it from falling down but the crane doesn't fall down after all the suits have self destructed.
Brandt identifies herself as DHS when she attempts to arrest Tony Stark in the bar, however, the badge she displays and later strikes the Sheriff with is a Drug Enforcement Administration (DEA) Special Agent's badge. DEA is a Justice Department Agency not a Homeland Security Agency and their past and present badges do not look similar.
When Happy is in the ICU the nurse adjusts the roller clamp to the IV fluid. A pump controls the flow-adjusting the roller clamp would do nothing except shut off the medication, causing the machine to call for attention.