Things spin out of Frank's control in "Chapter 21" and it's all due to his belief that because he speaks loudly and carries a big stick, he can't lose.
It starts when Remy visits Claire's old office manager, clearly looking for his own dirt since Seth isn't picking up any. The poor woman is working part time at a dentist's office and living so cheaply that Starbucks is a grand luxury. Remy -- being the slick bastard he is -- offers the woman a job at his firm, butters her up and then gets exactly what he was looking for: hints that Claire cheated on Frank last year. And this is where Claire got a little blind -- always mind your disgruntled ex-employees.
At the same time, Frank is meeting with leaders of a Native American tribe. They want to get federal recognition, so they can build a casino and Frank sees the word "Jackpot" floating over their heads, because he's sure this will threaten Lannigan's casino and get him to budge.
Somewhere outside of D.C., Rachel's plot is still a thing because her friend from church, Lisa, comes by in tears. Her girlfriend is doing meth again and since Lisa used to be hooked on both meth and heroin, she can't be around an addict. Rachel, being the lonely sweetheart she is, stupidly lets this girl stay with her and texts Doug a note about a guest "crashing" with her. If that's not waving a red flag and asking for trouble, I'm not sure what is.
Because Frank can't guarantee peace with Lannigan, he's still working on the bridge deal -- much to Linda's chagrin. She thinks it will look indecisive if the President reconsiders the deal, while he insists it will instill hope in voters. She rightfully notes that it's just a bridge in Long Island that no one will notice. She wants him to drop it and Frank agrees, but you know he's crossing his fingers behind his back (metaphorically speaking) the whole damn time.
Claire gets a visit from Megan, the army private who was also assaulted by General McGinnis. She's like a scared little rabbit, but she says she's certain she wants to speak out to the press and congress about her experience. Outside of the meeting, Claire pulls Tricia Walker aside and asks her to get the President to publicly support the bill, but considering the way he reacted when she asked him about buying wine for the Underwoods last episode, his cooperation is unlikely. Claire senses that the marital issues she stoked with her little Christina rumor are worming their way into Tricia's heart and suggests they use a spiritual advisor who (supposedly) helped her and Frank. Tricia thinks that's too risky, so opts to push a little harder for Walker's support on the bill instead. Bad move, FLOTUS.