Two Broke Girls/WMG

Caroline has a sister who will be introduced as a character at some point.
When Max confronted Caroline about her father's Ponzi Scheme, Caroline responded "He told us we were having a good year." Note that she said us, not me, meaning she wasn't the only one he kept in the dark about this. There's more than one member of her family. Now, she could have just meant her and her mother, but given the comedic potential of such a thing, I suspect that she'll be revealed to have a sister later on in the series.

Caroline and Max will fall in love at some point.
It seems painfully obvious that Caroline and Max are headed for a relationship at some point. Note the pilot episode where Max accidentally kisses a woman on the subway, perhaps foreshadowing? In episode two, they were already in bed with each other and Max claims that Caroline would be "the last les she'd be in." And even if it's not headed that way at this point, the writers may hear the fans, who are clamoring for Maxoline (Max/Caroline).

Martin Channing will be revealed to be a good guy all along.
This was hinted at in episode 4, when Caroline called him on the phone and said that "he can't be such a bad guy." Perhaps at the end of the season, he will get out of prison, and there will be the potential of Max and Caroline "breaking up."
 * Maybe not a "good" guy, but perhaps not as bad as he's made out to be. It's important to keep in mind that this is a guy who wasn't bothered by the fact that his scam probably ruined a lot of peoples' lives, so he's somewhat lacking in moral character. That said, it's already apparent that he genuinely loves his daughter and wants to make sure she's doing okay, so he probably doesn't fall into Complete Monster territory.
 * It wouldn't be a huge surprise if it turned out that he was a fall guy for his business partners, and was as much in the dark as Caroline was... although based on things Caroline has said, it would be something of a Retcon.

Johnny and Max will become a couple but break up... leaving him free to get together with Caroline.
It just seems like Johnny and Caroline have the potential to become the show's Super Couple. Plus they have great chemistry together.

Max and Caroline are an alternate universe Sam and Carly
It would explain the abundant Les Yay

Martin Channing will eventually be acquitted.
As a result, the feds will unfreeze his assets, and Caroline will be able to get her old life back. She'll decide, however, that she still wants to live with and be business partners with Max.

Martin Channing will get out of jail, but his assets will still be frozen
Once Caroline's truly addapted to being poor, he'll be freed and have to learn

Caroline's mother will show up at some point.
She told Max back in "And the Rich People Problems" that her grandmother had gotten rid of her mother "in a society way." But Caroline's mother is presumably still alive, and might use the disgrace of her ex-husband as a reason or excuse to reestablish contact with her daughter.

And, while we're at it, at some point Max's father will show up.
Because I said so.