To me, the important philosophical insight in the last stanza of this poem is that we are blind to our own faults.
The stanza is saying that we would change a lot of things about ourselves if we could see ourselves as others see us. It says that doing so would help prevent us from making a number of mistakes and would free us of silly ideas about ourselves.
I think that this is really quite true. We see ourselves as we want to see ourselves. Sometimes we give ourselves too much credit, sometimes not enough. But either way, it would be helpful to be able to see ourselves through others' eyes.
I don't know if I'd term it "philosophical," I'm not in that field, but I can explain the insight revealed in the final stanza of "To a Louse," by Robert Burns.
The turn of the poem comes between the second-to-the-last stanza and the final stanza you ask about. Before the turn Jenny tosses her hair, which reveals the louse in her locks. The implication is that she shakes her head and hair out of vanity. If she were not so vain about her hair, then, she would not have tossed her hair and the louse would not have been seen by anyone except the speaker.
After the turn, the speaker says that if we could just see ourselves the way others see us, we might be spared blunders and foolish notions.
The speaker applies this insight specifically to our obsessiveness with our appearance:
What airs in dress an' gait wad lea'e us,
And ev'n devotion.
We would be spared the putting on of airs that we do when it comes to our dress and walk, our appearance. And we would be spared of even our devotion--to our appearance.
Whether or not you want to apply this insight to other areas of one's life is up to you. But to make it apply to life in general might be a bit of a stretch.