Corrected entry: When Scott is running across the model of Pym Tech and getting fired at, one of the guards shooting at him just appears from nowhere. He wasn't in the previous scene.
Corrected entry: Paxton and his partner showing up in that family's back yard to tase and arrest Scott makes absolutely no sense. Firstly, they were following the helicopter. Apparently, they suspected there was someone in it they want to apprehend, but did they even know who or why. Remember, they know nothing about the shrink-tech at this point, and they just decided to leave the chaos at PymTech to follow it. Secondly, they decided that the briefcase, which they had somehow noticed fall out of the 'copter, was more important than whoever they were following in the 'copter (at night, no less). Thirdly, having decided the briefcase was more important, they somehow tracked it as it fell and went immediately to its exact landing point. It's difficult if not impossible to do something like that in broad daylight, let alone night time.
Correction: This is just a bunch of assumptions that all can happen. For your first point, PymTech had just imploded, so they would be following the helicopter for an explanation of what happened, considering there was nothing they needed to do at PymTech since the emergency services were there. For your second point, they followed the briefcase (which they probably did notice), because the helicopter was spiralling out of control and was going to crash, so they thought they might grab the only possible evidence they have to find out what happened at PymTech, as anything else would be destroyed in the crash. And for the third one, they had the general area of where the briefcase fell, so they just needed to follow the screams.
Correction: The other guard is the one Michael Peña knocked out earlier. Apparently the sound of gun fire woke him up.
MasterOfAll