Other mistake: When Agent Wells tells the White House they need to alert the Pentagon that Lozano is inside the Pentagon, she is told "it's already done, they are locking down the building right now." Then, later in the same episode, we see Lozano use a key card to easily pass through the building. (00:15:45 - 00:21:15)
Misalliance - S1-E19
Other mistake: When Patrick Lloyd receives the text message on his phone while working out, we hear it buzz and he reads it immediately but the message says "14 min. ago." The time also jumps from 12:15 to 12:59. (00:02:20)
Answer: The line of succession is VP, Speaker, President Pro Tempore, then the Cabinet Secretaries in the order the department was created. If none is qualified, then the Chief Justice or senior member if no Chief or Chief is ineligible or declines, acts as POTUS until either the House chooses a new Speaker or the Senate chooses a new Pro Tempore, whichever is first.