These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Audience-Alienating Premise: Hanks has addressed this in interviews, talking about how his casting was a deliberate step to get people too see "the movie about a lawyer with AIDS over the big puppet show" or some other less intense option.
A number of the previews made it clear it was a legal drama but gave no hint whatsoever of the actual subject matter of the movie.
Crowning Music of Awesome: Streets of Philadelphia. In both the music video and the opening of the movie, Springsteen shows the city in all its aspects — both the bright, shiny downtown landmarks, and the poor areas — minority, homeless, urban blight, and decay. And he ties it all together with this song. Streets of Philadelphia, indeed.
Some Anvils Need to Be Dropped: Similar to the Captain Planet episode that also dealt with this issue (albeit in a cleaned-up manner, as it is a kids' show), this movie drops the anvil that gay people and people with HIV or AIDS are no different from anyone else (a lesson that needed to be dropped back in the early 1990s, as a lot of people still had misconceptions about homosexuality and dealing with HIV and AIDS).
Unfortunate Implications: The film introduces the notion of the "homosexual lifestyle" being fundamentally risky and based around casual sex, yet fails to do anything to disprove this idea — though it should be noted that the film's writer, Ron Nyswaner is himself gay, and based a lot of Andrew's background and habits on his own, so it's highly unlikely he set out to be offensive in this regard.
It is Truth in Television to a degree. After the gay rights movement had begun but before the spread of AIDS it was quite common for gay men to be very promiscuous some believe as a way to reject heteronormative ideals like monogamy. This however largely caused the spread of AIDS within the gay community and killed off almost an entire generation of gay men. It's considered to be a great American tragedy.