I know "going to" and "present continuous" aren't always interchangeable. Are they interchangeable in this sentence:
Look! That plane is flying towards the airport. It [is going to land]/[is landing].
"Going to"—that is, the going-to future—and the present continuous are only interchangeable when used to talk about the future. For example:
I am meeting him on Monday.
I am going to meet him on Monday.
You can usually tell that a present continuous sentence is speaking about the future because a time in the future is specified somewhere in the context:
A: Do you want to go to the pub tomorrow?
B: I can't, I'm meeting Jane then.
Right now I can't think of a present continuous sentence that speaks about the future without also mentioning a time in the future. Using that rule, since your example sentence doesn't mention a time with the present continuous, it can be determined that the two are not interchangeable.
Specifically, your sentences would be interpreted as follows.
Look! That plane is flying towards the airport. It is going to land.
The plane is flying towards the airport, but it hasn't started to land yet.
Look! That plane is flying towards the airport. It is landing.
The plane is currently in the process of landing, but it hasn't landed yet.
I'm not sure of a situation where "going to do" and "is doing" are interchangeable. I think you may be mistaking the future tense:
I am going to eat lunch now
with the present continuous of "to go"
I am going to the shop to buy some lunch.
The first example is still future tense. It doesn't describe something in process, only something I plan to do (in the very near future).
The use of "to go" in the present continuous in the second example is a little ambiguous, since English speakers like to reduce "I am going to go to ..." to just "I am going" even for future actions. You can't tell whether this is something I plan to do (in the near future) or something I am currently doing.
After work I'm going to go to the store to buy us some groceries.
After work I'm going to the store to buy us some groceries.
These two sentences mean the same thing.
However, in the context of your example, it wouldn't be natural to say, "that plane is going to go to land." So "going to" will be future tense.
That plane is going to land. (the plane will land in the near future)
That plane is landing. (it is in the process of landing)
Note also this depends on context. If I say a plane is "going to land", unless I give some additional context ("in two hours", "in Chicago", etc.) we would assume it is about to land.