When they first reveal Dr Caldwell as a suspect - they flash his bio on the screen - and it already states he was abducted after the First doctor. They did not know he was abducted at this point yet.
When Octavio starts shooting at the SWAT team on the roof they return fire hitting one of the doctors behind Octavio. This would not happen in real life, the FBI's HRT is one of the most elite SWAT units in the world, they have a very similar training regiment as Delta Force and Navy SEAL's do, and they often conduct joint training with them. In fact most members of the HRT are former special forces, they are far too disciplined and experienced to return fire when there are civilians in the line of fire.
OA tells Valentine that the ear piece they are giving him is not visible unless someone looks directly into his ear canal. However it is clearly visible even from a side angle, and the antenna is sticking out the side, it couldn't be more obvious. They are using an old model from the 90's, the modern ear pieces the FBI uses are much smaller.