It seems that the most common complaint about the new design is that the site looks very similar to other sites. (Especially Mathematics was mentioned a few times, probably because there are many people who visit both MathOverflow and Mathematics relatively often. This was discussed mainly here: How can we visually differentiate MathOverflow from MathStackExchange within the constraints of the new design themes?)
From what I gathered so far, there are some options how to customize the look of the site, but it might take quite a long time before this happens. (Based on the comments from the CMs we are probably talking weeks or months.) It seems that at the moment the process is in the stage of collecting feedback.
One option is to make a few some simple changes now - ideally something that would at least help to distinguish the two sites a bit. (It would be probably best to leave the choice up to the Stack Exchange DAG team.1 Of course, they probably will take into consideration also the suggestion mentioned so far in meta.) And then - at some later point - a more thorough design change would come, taking into account the feedback from MO community collected here on meta.2
This could possibly help to satisfy those users who do not like the fact that the two sites look too similar. Some posts on meta suggest that at least some of the users are already becoming a bit impatient.3
TL:DR; What do you think about the possibility of making a few minor changes now - just to distinguish MathOverflow from Mathematics. With the understanding that this is only a temporary solution and a nicer design will come later.
2If you want you can look a brief discussion about this I had with Catija in chat. It was mentioned there that there is some stuff which can be mentioned relatively quickly. It starts at this message. (And there are also a few more discussions about the new design in chat - looking at the starred messages can give you a brief idea what was mentioned and of course you can browse a bit through the transcript from the recent days. Unless I missed something, the recent discussion of this topic in the MathOverflow chatroom started from December 13.)
3I will admit that it is difficult to judge to which extent the MO users are not satisfied with the new look - since we only hear from the users who came to discuss on meta. Probably most of the users that are perfectly fine with the new design did not bother to come to meta to express this.