In the sentence “He has already inspired some Filipinos to get up to their feet, and believe in an administration once more,” the word “and” is actually not a coordinating conjunction; it is an additive function word that compounds the prepositional phrases “to get up to their feet” and “(to) believe in an administration once more.” That sentence is therefore a simple sentence, not a compound sentence, and that comma shouldn’t be there at all because its presence truncates the sentence, weakens the additive power of “and” as a function word, and makes the meaning of the sentence ambiguous. Indeed, because of that comma, it is unclear what the operative doer of the action is in the phrase “believe in an administration once more.” Is it “he” or “some Filipinos”?
See how that ambiguity disappears when that comma is dropped altogether: “He has already inspired some Filipinos to get up to their feet and believe in an administration once more.” In this comma-less construction, it’s clear that the doer of the action for the two prepositional phrases is the noun “some Filipinos.” It also clearly indicates that what we have here is a simple sentence, not a compound sentence, and that what follows the direct object “some Filipinos” is a compound prepositional phrase—meaning two prepositional phrases compounded by the additive function word “and.”
Even if not grammatically necessary, however, putting that comma sometimes becomes advisable for the sake of clarity. This often happens in news journalism, particularly in the case of simple sentences with an extended compound predicate, as in this example: “He has already inspired some Filipinos to get up to their feet and believe in an administration once more, and managed to come up with well-thought-out reform programs without being challenged in the courts of law.” Here, the comma before the second predicate (“managed to come up with well-thought-out reform programs without being challenged in the courts of law”) serves as some sort of demarcation line or signal that what follows is, in fact, a second predicate rather than part of the enumerated actions whose referent noun is “some Filipinos.” It must be noted here that the sentence in question here is, like the first example we examined, a simple sentence, one consisting of a single doer of the action (“he”) and two compounded verb phrases (one the verb phrase with “inspired” as operative verb and the other with “managed” as operative verb).
In the case of compound sentences, it is grammatically mandatory to put a comma between the first coordinate clause and the second coordinate clause. Thus, the use of the comma in the sentence you provided as example is correct: “Filipinos now can tell an act from an act, and political leaders have the social responsibility to be honest to their constituents.” In this case, the comma is functioning as a coordinating conjunction, in contrast to its function as an additive function word in the first two examples we evaluated earlier. We can see that the presence of the comma not only creates a clear demarcation line between the two coordinate clauses in a compound sentence but also signals a momentary pause that makes it easier for readers to comprehend what the sentence is saying.
In practice, though, news reporters and editors tend to eliminate the comma between the coordinate clauses of compound sentences. It’s a breach of good grammar that makes their news stories tougher to read and understand, and we can only hope that they will realize this and make sure to supply that comma everytime it’s needed.