Feeling Alive
One of the reasons old Billy is so upbeat and optimistic despite his age is because he -- unlike members of the younger generation including Archie's children -- has had a chance to reach the top of his profession. A celebrity in his own day, and far more successful than his son in show business, Billy got out of the music-hall performance industry before it started its long downhill slide into obscurity. He therefore has memories of his successes to reflect on. Unlike his son Archie, Billy believes he truly got to live and to feel alive.
Archie says sometimes that he feels "dead inside" and that he feels nothing. He believes that it is his lack of emotion and human connection that causes his acting and comedy to be fake and uninspired. Having never reached any particular significance as an actor or impressario, Archie lives in a world with very little hope and seeks solace in the arms of random women. Heedless of the consequences of his behavior on others, Archie believes he has been deprived in some way. He is not sure exactly who held him back, or from what, but he feels as though his opportunity to truly feel alive has been stolen from him.
Class
Billy does not give the impression of belonging to any particular social class, but he sent both of his sons to an extremely expensive school where they mingled extensively with young men of a higher social class. In the case of Brother Bill, the elder son, the expensive education paid off and set Brother Bill on the path to becoming a successful barrister (in American terms, a litigating attorney). Archie, who received the same education, retains some of the trappings of a higher class such as an educated vocabulary and a slight tendency to be pedantic, however he surrounds himself with people of a noticeably lower class than himself. Phoebe, for example, uses common terms such as "blimey". She and the children frequently overindulge in cheap gin and act out various lower working-class stereotypes.
Jean is initially ambiguous in terms of her class presentation, particuarly in conversation with Graham who appears to be a younger version of Brother Bill bound for a similar career. However by the end of the play she identifies more completely with her family than with her would-be husband, and chooses to stay with Phoebe and move with her to Canada rather than continuing her engagement.
Pride
The play is set during the Suez Canal crisis, which is indicative of an overall loss of international power and prestige for Great Britain. The British Empire, having reached its zenith during the reign of Queen Victoria, is gradually collapsing. The bombing of World War II is still very fresh in living memory, and the English economy and infrastructure is still rebuilding itself while being overtaken by other industrial nations such as the United States that did not suffer the prolonged physical bombardment and loss of life. When Mick is murdered by his captors -- an unthinkable act of barbarism that shows complete contempt toward the waning British empire -- the nation's sense of shock and outrage briefly affects the Rice family as well. But the decline in British fortune parallels the decline in the music-hall business that supports Archie Rice, his wife, and sons. Indeed, the music-hall no longer provides enough revenue to feed and house the family, so Billy Rice has been contributing money for a long time to keep the family in their very limited and unsatisfactory dwelling.
The end of the final scene is ambiguous. Archie Rice has an extended monologue, quite possibly to an empty theater, and Phoebe appears with his rain hat and coat, which he puts on. He appears to leave with her, then the lights blink out, they disappear off the stage, and the stage is empty. Archie Rice is gone, but the music remains. It's possible that Archie stayed on in the theater to hold out as long as he could before being sent to prison, but the stage instructions suggest that he left with Phoebe for Canada, swallowing his pride and accepting what he believes to be a boring and disappointing future.
Attention
Many people in the play want the attention and respect of others, but the more they do to command it, the less of it they receive. Phoebe, for example, talks aimlessly and listens to nobody, but is not taken seriously by anyone. Even in the penultimate scene, two related but independent conversations occur, one between Jean and Graham and the other between Brother Bill and Archie.
When anybody tries to hold Archie accountable for something he says or does, he turns it into a joke. It's as though his life is one neverending comic routine wherein he never truly has to answer for the harm he does to others. He can continue living in his fantasy world wherein he's a successful showman like his father, and where the mundane realities of his legal and economic trouble don't matter or can be laughed away. He deals with his difficulties by ignoring them-- by withholding his attention or by pretending to be "dead" or immune to the feelings they generate. Only when his son Mick dies does he have to confront reality. When this happens, words fail him and he finally has to pay attention to how he feels.