Deliberate mistake: There are several large security mistakes that were obviously added to the film to move the plot forward. The takeover of "Control" would not happen that way. The Secret Service keeps it in a secret off site location which not even the security detail knows. This location is in some kind of very remote bunker to prevent what happens in the movie. Secondly, when the threat is identified and the switch to the double is made, the President would have been moved to a secure bunker created for the purpose until the threat was dealt with.
Suggested correction: It actually could still be possible for a takeover of "Control" to happen even if it was a secret off site location/secure bunker. Depending on Taylor's security clearance and how high up he is in the secret service, he could have been one of the few in the security detail that knew where the secret location was. Since he's the one that got Barnes back on detail, he most likely has a high clearance.
No actually it couldn't be possible for takeover of control. No one in the security the detail knows where the secret location is. Even if Taylor had a high clearance it only grants access to a limited number of places. One of the places it doesn't grant access to is the secret location.
With a high enough clearance it could still have been possible. Not to mention there could have been more than one mole in the secret service other than Taylor who had the clearance to know the locations.
Read it again. "Even if Taylor had a high security clearance it only grants to a limited number of places. One of the places it doesn't grant access is the secret location." So Taylor would not have access to the secret location no matter how high his security clearance was.
Takeover control couldn't be possible if the location was an the location an off site secret bunker because the villains wouldn't be able to find it. Even if Taylor had a high security clearance he wouldn't know where the secret bunker because if he was ever allowed in there he would blindfolded to prevent him from learning where the bunker was. Taylor would get arrested if he learned where the bunker was.
Only the service officials know where the bunker is. Taylor is not a secret service official.
Plot hole: It stretches credibility that the little girl wanders quite far away from the plaza and ends up on a busy road, and her mother just happens to be nearby.
Suggested correction: Anna wasn't following her mother. Her mother got separated from her in the chaos and when Howard carried her to safety, she saw a woman who resembled her mother leaving the plaza. She then ran in the general direction of the woman and it just so happened to be the same direction that Howard was running and ended up in.
Also, it isn't entirely out of the realm that her mother ran in the same direction as them both prior to Anna seeing her since she was out of the plaza before Anna and Howard were.