I haven't seen it in quite some time, but I remember nearly the whole plot confusing me (though not entirely in a bad way). So maybe that was SOME of the podcast host's problem (I don't know since I haven't seen the podcast).

Nearly the only thing that "makes sense" to me is Barbara Rhoades' halter top!

"I do not understand the whole Steinmetz thing at all, or why Brenner needed Lawrence Melville at all. "

Brenner was acting as a double agent to extort money from the agency for his own benefit. Brenner creates the "game" for the CIA to play by using a "missing naval code on microfilm" that's in the hands of some boogie man (Steinmetz, the other half of Brenner). Because Henderson wants his due share of money from Brenner on past deals "down in bananaland", Brenner uses his double-agent hoodwink yet again to not only rub out Henderson, but to make even more money on the fake microfilm crisis. So, Brenner sets up the deal with the broken poker chip and money changing hands (money from the CIA) to cash-in on the "crisis", then later has to take-out Melville since Columbo has his name from a witness that saw him leave Sinbads.

The cigarette machine click-click move was to alert Melville to the party he had to meet. The move was to keep all parties "in the dark" and partitioned using coded actions. This keeps the two unsuspecting players (Melville and Henderson) assuming there is truly an elaborate plot with multiple parties involved exchanging large sums of money, etc. All part of the double-agent's psy-op tools to pull one over on his boss and everyone else.