First of all, observe Tom's affair with Myrtle Wilson. It's clear that if things were going well in the Buchanan marriage, then Tom wouldn't be fooling around. To make matters worse, Tom makes no effort whatsoever to hide his numerous infidelities. In fact, he insists on parading his current mistress around in front of his friends like a badge of pride.
Daisy's brief fling with Gatsby is also a sign that all is not well with the Buchanans' marriage. Even though she knows that Gatsby isn't the right man for her, Daisy still goes ahead and has an affair with him, largely as a way of escaping the cramped confines of her unhappy marriage. But despite everything, she cannot and will not leave Tom—not least because, as a crashing snob, she couldn't possibly contemplate spending the rest of her life with a social-climbing parvenu.
Then there's the matter of domestic abuse. As well as being a serial philanderer, Tom is also an abuser. Everyone can see it from Daisy's bruised knuckle. Given the brutal manner in which Tom breaks Myrtle's nose, we shouldn't be surprised that he resorts to physical violence with his own wife. This is further proof, if proof were needed, that the Buchanans' marriage is not a happy one.