This is something that has varied with time. I believe that it was once more common to include dots in initialisms (such as F.B.I.) or acronyms (such as U.N.I.C.E.F.), but I think you'll have a harder time finding contemporary news articles with acronyms or initialisms using dots like that nowadays – at least, it was easier for me to find articles with letters in all caps (e.g., FBI, UNICEF).
For example, on a UNICEF website, a Wikipedia page, and in article found in The Atlantic, all usages of the acronym are spelled as UNICEF (no dots), and many other abbreviations can be found in a similar form on those same pages, such as CEO, IGO, IFRC, UN, and NASCAR. That said, the Wikipedia page is a little inconsistent in this regard with respect to the abbreviation FC (football club): Sydney FC is listed with no dots, while Olympiacos F.C. (from Greece) and Rangers F.C. (from Scotland) are listed with the periods included.
The Grammar Girl blogger says this (emphasis added):
There's no strict rule about putting periods after each letter in an acronym or initialism. Some publications put periods after each letter, arguing that because each letter is essentially an abbreviation for a word, periods are necessary. Other publications don't put periods after each letter, arguing that the copy looks cleaner without them, and that because they are made up of all capital letters, the fact that they are abbreviations is implied.
In the past couple decades, contemporary typesetters seem to be favoring "cleaner" conventions. One common exception seems to be U.S., but that may be in part because of its similarity with the word us; consider these two sentences:
U.S. lawmakers debated the matter late into the night.
Us lawmakers debated the matter late into the night.
US lawmakers debated the matter late into the night.
The first two are easy enough to figure out, but some might argue that the third one could be confused with the second.
A different blog post from the Grammar Girl says this:
In American English, we always put a period after an abbreviation; it doesn’t matter whether the abbreviation is the first two letters of the word (as in Dr. for Drive) or the first and last letter (as in Dr. for Doctor).
British writers, however, make a distinction: abbreviations that are written with the first and last letter of the word (as in Dr for Doctor and Mr for Mister) do not get a period.
Heavens to St Peter! This just goes to show how muddled conventions like these can be.
Best Answer
The sentence uses three clauses and has the structure:
The author could have written:
A, and B, and C.
Mr Trump is the president, and 47% of Americans trust him more than they trust the media (according to a Quinnipiac poll), and his charge against Mr Obama was grave.
However, usually we prefer only to use the word and before the last item in the list. We put a comma between the first two items to show that they are part of the same sentence. We understand a silent and there, even though we do not write it or say it.
The writer has put these three clauses together like this because they form a list of three things which—when we consider them together—provide evidence for their claim that "some sort of follow-up is necessary".