Beautiful Mistake

Yeah, of course. It's a much-hated episode for good reason, and not only are there problems within the episode, but they dug themselves a hole that they really struggled to get out of afterwards.

I'd make some of the violence Rio engages in during S1 and S2 more explicit rather than implicit (on-screen instead of off-screen) because some portion of the audience never saw him as a real threat, but Beth did, and that disconnect impacted people's ability to understand Beth's impulsive decision-making in the scene

I'd extend the dialogue in the scene and/or include a rapid flashback sequence that illustrated Beth putting the exact pieces together that Rio was setting her up as his fall guy—and I'd probably explicitly draw this parallel when the concept came up in s4 as well; throughout the season, Rio used her family business with her name on it to smuggle pills, put his counterfeit cash in her name in a traceable storage unit, and kept a dead body (he made the girls pay $200k to retrieve) he believed they murdered stored in the same grocery store where her sister worked. He was keeping his own hands clean while using Beth's name pretty publicly, and while it makes sense as a punishment for her getting him arrested in s1, it also makes sense for Beth to be hurt and betrayed.

I'd change the kidnapping scene. Either explicitly make it a miscommunication between Rio and his boys or find an alternate way to raise the stakes and have Beth be emotionally distraught and scared in the scene, since those emotions were necessary to the outcome of it. I just simply don't believe Rio would have kidnapped her—even if he was pissed off she wasn't answering her phone when the stakes were so high.

I do think Beth needed to feel physically threatened by Rio to ultimately react and pull the trigger, but I'd cut out Rio calling her a bitch and lunging at her; it felt OOC since we'd never, ever seen him act like that before. Even when he was behaving violently, he was cool and under control. I don't know how I'd fix it, exactly, but maybe if Turner had been able to talk in the scene, that could'be escalated tensions somehow? I dunno.

Shrink, reduce, and change the framing of Rio post-shooting.

Either way, if he presented her as Beth it would mean her name is sacred to him EVEN in front of his family (whom he LIVES for) OR that he feels COMFORTABLE enough in their relationship (or at least showing he is for the purpose of 406's plot but we know everything they try to pass as a game are actually real feelings) that he can share her name with his family? It would feel HUGE. To never say her name in front of everyone else but her, but then INTRODUCING her as Elizabeth to someone ELSE? It's like marry her already.

Anyways, idk if that makes a lot of sense. There's a lot to think I think.

I think this question hinges a lot on your interpretation of the scene at dinner when Nick calls Beth “Elizabeth.” We can either infer:

Nick was telling some version of the truth and that Rio had talked about her before, using the name he uses with her in private

Nick overheard Rio introduce Beth as “Elizabeth” at the party and wielded it here

Nick overheard Rio call Beth “Elizabeth” at the party and wielded it here

I personally would rule out the first and second choices.

Nick is lying in the scene—he says that he’s heard a lot about Beth, but the rest of the season suggests otherwise. He doesn’t seem to know about their prior partnership, the shooting, the supposed pregnancy, Lucy, or understand even a fraction of the real feelings Rio has for Beth—and Rio gets tempted into flaunting their sexual relationship the second Nick suggests it hasn’t yet been consummated. He’s both private about their relationship but unable to let there be any indication that it’s less than what it is, so I don’t think he went around talking about her easily prior to this scene.

Rio also gets possessive in the scene when Nick tries to intrude upon this thing—the name—which is theirs, as indicated by the hand on her back. That could be because Beth prompts it by firmly naming it as just between them when she corrects Nick, but I think it’s more than that. Nick seems to know that he’s touching a nerve when he says it the first time, and he presses harder by saying it again. That suggests to me that he’s already picked up on something with the name.

That could mean that Nick heard Rio introduce her as Elizabeth—and heard Beth correct people like she corrects Nick—but I don’t think so. The correction is a loaded moment here. And, like you said, the implications of Rio using this name he uses with her mostly in private (he never uses it in front of Annie and Ruby, but uses it in front of Dean for the suggestion of its intimacy) would be significant when introducing her, so it would be odd not to show it.

So my conclusion is that Rio didn’t introduce her, but let her introduce herself. I think this aligns with Rio’s treatment of her—it both gives her agency in how she wants to be known among his family and it leaves the hard part of defining their relationship up to her. It’s a gift and a sort of punishment—classic Rio.

I suspect Nick had his eye on Beth from the moment she arrived though, and I could see Rio slipping in a private “Elizabeth” that Nick overheard. Unlike Nick, Rio doesn’t code switch between the two names depending on situation or audience—the drop in 2.10 is the only time in the series that suggests he ever does, and it suggests possessiveness or privacy about including others in the sort of “ritual”—so I don’t think he introduced her as “Beth” and I do think him using “Elizabeth” in a moment he thinks is private something that could feasibly happen.

GOOD GIRLS APPRECIATION WEEK || DAY 4 || LOVEBIRDS

Baby, though I’ve closed my eyes I know who you pretend I am I know who you pretend I am

Rio approaching Beth.