What are the signs that Tom and Daisy have a bad marriage?

One of the first signs that Tom and Daisy have a bad marriage comes in chapter 1, when Nick visits Tom and Daisy for dinner. Daisy shows Nick her little finger, which is black and blue at the knuckle, and claims that Tom hurt it. The only way someone can cause another to bruise, especially the pinkie finger, is to grab the hand extremely hard. Tom never hurts Daisy physically through the rest of the novel, but he does not hesitate to break Myrtle's nose in chapter 2, so the audience can conclude that he is at least capable of such violence.
It is also in chapter 1 that the audience learns that Tom has a mistress, because she calls during dinner and he takes the call, in front of not only his wife but also Nick and Jordan Baker. Tom does not try to hide his mistress, and in chapter 2, he shows her off to Nick in New York.
Daisy is not shy about showing off her own affair with Gatsby in chapter 6, which causes Tom to investigate Gatsby and where he attained his wealth. But that affair is probably the only one Daisy has had up to this point in the story. Tom has had many affairs, even during his honeymoon with Daisy—in chapter 4, Nick recounts how Tom was in a car accident with a chambermaid as his passenger. In chapter 7, Daisy even mentions an affair in Chicago, which is why they left and moved to New York.
So, Tom and Daisy's marriage is bad from the beginning, and it never seems to improve through to the end of the novel. However, they are destined to stay together in misery.