For a weak spot in Levinas one can point to his political theory, or better: the complete lack of it. That is not to say that Levinas does not care about the rule of law, parliamentary democracy, or the public debate. On the contrary, he makes clear at several places the importance he attaches to these achievements, which he often refers to as ‘Institutions’.
But perhaps his frequent use of that term indicates the boundary of his interest. The existence of those institutions is of immense importance for him, but essentially related issues such as power play, public speaking and performance, or rhetorical communication can captivate him less. In any case, he did not write about them.
However, these latter elements constitute precisely the area where Hannah Arendt feels at home. The political praxis in the public space is for her a stage on which we realize ourselves and the communal life. At the political scene everyone gets a chance to show who he is, and there a multitude of voices can shape politics.
This is a catchy vision, especially because it assigns to democratic politics the task of doing justice to the individuality of people. And instead of arriving at a simplistic thinking in terms of majority-versus-minority it seeks after true pluralism.
But at the same time she perhaps has a bit too much faith in the possibilities of noise-free communication and of presenting oneself to others. That has to do with her deep-rooted confidence in reason to which mature, educated people have access and which can serve as infallible tool for the organization and content of the required communication.
Apart from the caveat that can be made that Arendt’s utopia requires highly skilled individuals, Levinas shows us this other blind spot in Arendt. Namely the fact that reason is perhaps not as reliable as she thinks it is. Because according to Levinas reason permanently produces illusions and therefore misunderstandings. Not because the people participating in politics and debates are malicious (although that could in addition be the case), but because reason according to Levinas has a somehow autistic character, which one cannot, again with the help of reason, eliminate just like that.
For unmasking of these illusions Levinas refers to the appearance of the Other, because he – the injured one – can make us aware of them. Maybe not necessarily by his appearance in public space, and with less glare than Arendt attributes to ‘showing yourself’. But with at least as much power and an equally large contribution to the plurality of the community.
Also see Totalitarianism is with us and Why Heidegger doesn't bring us any further