"The Roaring Twenties" refers not only to the decade of history, but Eddie's twenties. He starts the movie fresh out of the war, presumably a teenager or in his early '20s, and must be in his '30s at the end.
Eddie himself is a fairly obvious symbol for America throughout the movie: starts off beaten down from the Great War, then becomes prosperous in the '20s but also in denial about the problems sneaking up on him (Jean's affair receiving the most focus), making a humiliating finish, and ultimately dying completely.
Panama nudges Lloyd and Jean to hook up behind Eddie's back, and herself hits on Eddie. It looks like a conniving plot to free up Eddie for herself, but she's also doing it for Jean's sake. It's clear Panama cares about the poor girl, when she says "I hope she can outrun him (Eddie)." She knows a nice girl like Jean will only get her life ruined by hanging out with Eddie. She tries to convey to Eddie that he and Jean are not each other's type ("Your used to running around with, well, with girls like me!")
Every single scene between Jean and Eddie emphasizes how Jean is a person who is able to move on, and Eddie is constantly in denial. When he first meets her, he is disappointed because he'd assumed she was an attractive adult professional going off vague information from her letter and photo, and she's naturally crushed by his rejection. The second time they meet, a few years later, she's almost completely forgotten about him, and focused on her show career; Eddie refuses to believe she's serious about show business, and keeps trying to get her to "admit" that she's really just waiting for Mr. Right. When he drops her off at home and she mentions her mother dying, it seems like a throwaway line, but it's really highlighting the most important trait of Jean's character, when she says calmly that her mother's death was a long time ago and she's over it. In the scene where Eddie gives her a ring and proposes to her, it couldn't be more obvious that Jean's answer is ''no't' "yes," and once again, Eddie is in denial, and insists that she's just worried about his being a gangster, and tells her to hold onto it until he goes straight. George's pointing out the obvious attraction between Jean and the lawyer enrages Eddie, because it's the only time so far that anyone has confronted him about the obvious issue in front of him. By the end of the movie, when Jean is a housewife and seems to have lost interest in her career, it's undoubtedly because she realized she wasn't a very good singer (Eddie bribed the speakeasy to "hire" her), and got over it. And obviously, she got over Eddie.
It's heavily implied that Eddie is the father of Jean's son. The implication is made clear when Panama asks him, "Who does the kid look like?" and he dodges the question, answering, "Like her." Fact is, that kid looks like Eddie, at least a lot more than Jean's husband Lloyd. Re-watch the scene where Eddie meets Jean's son, and the implications become evident; the kid has a violent streak like his father, and when he brags "I killed three Indians!" his mother's smile falters, as if she's afraid he's becoming like the wrong "father." The situation appears to be a rehash of Jean's secret affair with Lloyd years earlier; everyone secretly knows what's going on, but no one is saying it. The fact that Eddie is killed shortly after only adds to the Fridge Horror, as one wonders when, if ever, the boy will learn his true parentage.