Colin's answer is right, except that I see — in line with avid's comment — that the different temporal focus indeed indicates a small difference in meaning.
When I say "wasn't it supposed to start 30 minutes ago" I talk about the actual start. A good example would be fireworks where the start would be an event in itself, and everybody is waiting for it.
By contrast, with "wasn't the talk show supposed to have started 30 minutes ago" after switching on the TV I'm focusing on the ongoing talk show after it has started, and less on the start proper.
When speaking casually one could use both tenses interchangeably. I also made an effort to use two examples where the difference really mattered (fireworks have a spectacular start, talk shows do not), which is often not the case.
7While the two are definitely interchangeable, I think there is often a different shade in meaning. One might use '...to have started...' to imply that this hasn't happened, e.g. "Why isn't the class running? Wasn't it supposed to have started 30 minutes ago?". '...to start...' is more appropriate in the case where you presume it has happened: "Why aren't you at your class? Wasn't it supposed to start 30 minutes ago?" – avid – 2020-03-21T02:13:14.393
@avid that's was helpful to me, I think it would be more useful as an answer – briantist – 2020-03-21T03:10:56.560
7The contextual preceding sentences are not the same. @avid says they’re different shade in meaning, but look what happens when they are interchanged. “Why isn’t the class running? Wasn’t it supposed to start 30 minutes ago?”— here “to start” would also imply it hasn’t happened. Let’s look at the other; “Why aren’t you at your class? Wasn’t it supposed to have started 30 minutes ago?”— you can presume it has happened here with “to have started.” But really it’s not the verb tense, It’s the preceding sentence that is changing the meaning. – vol7ron – 2020-03-21T11:57:15.343
@vol7ron I think Avid is trying to say that they feel that it's more appropriate to have the sentences that way around (i.e. "supposed to start" fits better with the "why isnt [...]", and "supposed to have started" fits better with "Why aren't [...]"). I sort of agree, but i'ts a pretty minimal difference. – BeB00 – 2020-03-22T09:12:43.057
@BeB00 you might be right. I’m not a linguist, but I still think that’s left to preference, which leaves it interchangeable in my mind. In both cases, I might default to “supposed to start” as a manner of preference. There probably is something more than meets the eye, something more technical, which we haven’t identified that would distinctly determine one over the other. I was going to say the rhythm or meter of the sentence might affect my preference, but I’m hoping for something more that could be explained in the confines of a comment, which might circle back to @avid’s original comment. – vol7ron – 2020-03-22T13:53:40.907
1I'm sure if I sit here and stare at the two constructions long enough I could convince myself there's a slight difference in meaning, but I'm guessing that if you gave two groups of people a paragraph to read and one group saw construction 1 and the other group construction 2 there wouldn't be a significantly different interpretation of the text between the groups. – eps – 2020-03-22T18:28:29.263