Upon further analysis, it appears that the point about Domino being HIV positive is important to the plot for a number of reasons.
One, there is a common thread in the film involving the combined themes of sex, lies and death, which come together quite perfectly when one considers that sex can actually lead to death in the form of potentially life threatening diseases (i.e. HIV), and that Bill only decides not to go through with sleeping with Domino after he has to lie to his wife about why he’s taking so long.
Two, Bill uses his power as a doctor (in particular in the scene at the diner) in order to gain access to people, informing the waitress that he has results from some tests that Nick will want to know about (more threats of death and lies). This is important because Domino receives real results from a test that have real implications for her.
Finally, Bill always appears to be thwarted (by himself or others) at every turn when attempting to cheat on his wife. Sally knows he might have slept with Domino so she has to tell him that Domino has HIV and that effectively kills any possibility that they might have sex. Of course, Bill could say that he didn’t have sex with her but that doesn’t really matter and brings up another plot hole which is that Sally says Domino told her how “nice” Bill was to Domino the night before.
If she really knows the truth then she knows that Bill didn’t have sex with her. If that’s the case, why even bring up the HIV? Anyway, sex, lies, and death IMO are the major themes and I’m not sure they’re supposed to be perfectly woven together just used more broadly as devices to inspire the viewer to think more deeply on the subjects.
Also, I noticed that the paper Bill is buys after finding out that Domino is HIV positive says LUCKY on the front page and this is about all you can make out concerning the headline. I think there’s a lot more going on in this film than meets the eye!