Factual error: When Frank talks to Booth the first time on the phone and realizes he's at the phone outside, he runs to find him, only to find the handset swinging and the phone emitting the periodic screech that is heard after 1 minute of leaving a phone off hook. Seeing as how the apartment is three stories max, there's no way that sound would be playing by time he got there even if Booth somehow hung up first. Furthermore, even if it did take that long, the handset wouldn't still be swinging.
Factual error: The second time Frank speaks with Booth, the line is being traced. When Frank switches over, Okura tells him to keep Booth on the line until they get the ANI (automatic number identification). Assuming the secret service has access to the phone company's internal computer (since you have to have toll-free service or be a customer of an ANI outsourcing company to receive the subscription based info), ANI only says who the phone is registered to and since the call was being tapped they would've had the ANI information before the call was picked up. This still holds true if the ANI is faked by a well built PBX system (as said later).
Continuity mistake: In the breakroom scene where Horrigan is thought to have had a heart attack, the EMTs burst in and attempt to "revive" him and he shoves them away to both sides. The camera then shifts to an over-the-shoulder view, where one EMT says "I got a call there was a cardiac case." Both EMTs are present at the left and right edges of the screen. Seconds later, Frank says "Oh, I get it. Who's the wise guy?" and stands up. In that brief interval, the EMTs have vanished completely; when everyone else files out of the breakroom, laughing, they are nowhere to be seen.
Continuity mistake: When we see Frank peering out of Booth's window after the landlord calls the cops, it appears to be dark outdoors with only street lamps for light. The camera then cuts to Booth viewing Frank from across the street, but it appears that it is now daylight outside.
Factual error: When the motorcade arrives at the hotel, the Secret Service agent opens the door to his limousine and the President gets out. The door is then almost immediately shut. Proper procedure for the Secret Service is to hold the door open until the President is well away from the car, in case of an incident where the President has to be evacuated from the area quickly.