The challenge in the question is that there is not merely one thematic aspect to the poem. Yeats' poem is so intricate because it represents so many different themes within it. On one hand, there is the theme of decay that is so compelling throughout the first stanza. The critical examination of this theme would reside in the images Yeats presents in the exposition of the poem. The "widening gyre," "the falcon cannot hear the falconer," as well as the "anarchy loosed upon the world" are all such images that show a world in chaos, a sense of being that is rootless, subject to absolutely everything negative and little positive or redemptive.
Another critical examination of a thematic element in the poem would reside in the notion of Christian redemption. In this examination, a study of the second stanza would be appropriate. Yeats' critiques the notion of "waiting" for a second coming, a hope at redemption that prevents a sense of action being taken. One can almost see a critique of paralysis that results from this notion of "waiting," as no action is taken towards this beast who "slouches towards Bethlehem." In this critical examination, Yeats is forceful in how religion, especially that of the Christian notion of redemption, is not necessarily evident in the time in which he is writing. I think that these two critical examinations help to bring out the thematic applications of the poem and help to explain why the poem is so powerful and compelling as both art and social critique.