Shakespeare uses fools very creatively. They often seem to use their apparent role as a fool, as somebody who speaks nonsense, as a shield that actually allows them to speak truth and wisdom. However, it is often not recognised as such by the characters who listen to them and expect only foolery to leave their mouths. The Fool in this play is no exception, and you are right to indicate that at various stages he comments on Lear's initial disastrous decision to be flattered by his two eldest daughters and fail to see the genuine love of his third daughter, Cordelia. Note what he says in Act I Scene 4 when he first appears when he urges Lear to take his "coxcomb," or his cap:
Why? For taking one's part that's out of favour. Nay, an thou canst not smile as the wind sits, thou'lt catch cold shortly. There, take my coxcomb. Why, this fellow has banished two on's daughters and did the third a blessing against his will. If thou will follow him, thou must needs wear my coxcomb.
If we look carefully at this speech, we can see how the Fool is quite openly mocking Lear for his decision. It is Lear that is "out of favour," and therefore unpopular, and the Fool mocks Lear's decision by saying he actually blessed Cordelia, even though he didn't want to do it, by banishing her. The Fool ends by assuring Kent that he would need to wear the fool's hat if he wants to follow Lear. Clearly he is questioning Lear's actions and saying they were very foolhardy.