After Ratchet says that no one is allowed to ask about where Bigweld is, one robot says that they'll all see him at his annual ball. Ratchet's response is to open a trapdoor underneath him. When the Bigweld Ball comes around, Bigweld doesn't show up.
When Rodney accidentally predicts the angry mob, Fender begs him to ask for money to fall from the sky. This isn't just Fender having a get-rich-quick scheme. He wants money to afford upgrades and avoid being outmoded.
Mr Copperbottom having failing eyesight to the point he needs glasses in his later years might seem odd seeing as he's a robot that can replace broken parts. But remember, his warranty is expired, and his family is so poor that his son has been getting hand me down parts for years. He probably has glasses because his eyes are wearing out, but they can't afford to replace them.
The ingots that come out of the furnace actually make a pretty good symbol for Bigweld and Ratchet. While the ingots are shiny and new, they're clearly made from pot metal, which is a cheap alloy that tends to form interior defects when cast. Bigweld and Ratchet are shiny on the outside and present a good public facade but they have interior defects in terms of their personality.
Alternatively, it could represent the superficial nature of the upgrades Ratchet is selling; all the shiny new upgrades in the world won't conceal a terrible personality.
There are robot dogs and birds and such, but we never see anything organic - not so much as a blade of grass. Was all life killed off by something in the now-distant past, leaving the robots play-acting the roles of their old masters?
In this universe, the parents make the baby out of parts. We know that some parts get reused, as the Copperbottoms are known to have used pieces of their parents (hopefully old ones they didn't need anymore!) for Rodney, and his cousin gave a younger Rodney some hand-me-downs. Madam Gasket says later on though that she stole parts for Ratchet. Therefore, it's very possible that she killed other lower-class bots to even make her son.