First of all, I really like the concept of the new Core Mathematics section. It is indeed a huge improvement, because like you said, the surprise effect of weekly problems works great for olympiad problems, but not for core subjects. There are some things that I would like to point out, though.
I found several bugs. When I complete set 1 (successfully) on a certain subject, and I click on set 2, it at first shows me the first problem of set 1 with the solution shown (so basically what I saw right after answering that problem), and clicking on 'Next Problem' results in viewing the second problem of set 2, rather than the first.
Also, after completing both set 1 and set 2 of a certain subject, it sometimes shows me the technique screen (with all sets on it) with set 2 on the left and set 1 on the left, so it swapped their positions. However, sometimes they are in the correct order. It's not really a problem, but I don't think it's intentional.
I think there is also a bug in the star system. I'm not sure if I completely understand it, but this is how I think it works: the amount of stars you earn for a certain topic depends on the most difficult set you've successfully completed. Correct me if I'm wrong. I successfully completed the first two sets of both basic and intermediate prime factorization, and I only got one star. I even completed one advanced set (so I think I should get three stars, rather than one).
The unit in which to answer the problem isn't always mentioned. It was really clear from the context, but I still point it out because usually it is mentioned. Also, it once said 'in minute' rather than 'in minutes', I don't remember which problem though.
Now, about the necessity to invite friends on facebook to unlock additional sets. I know I'm not the first one to point it out, but I also don't think this is the way to go. I think I can manage to invite several facebook friends, but I know many Brilliant users will not. Alexander S. pointed out it would be good if we could buy sets with points, and I think that is a great idea.
I'm not sure if the problem submit form also works for the Core Mathematics problems, but if it does, that would be great. It might be an idea to be able to specify the topic and level of a problem when submitting it. If you do this right, I'm sure the Brilliant community can make tons and tons of great problems for every difficulty. Although there is a broad range of topics already available, the amount of problems in a topic is sometimes very little, and I'm sure many users would love to contribute.
That's it for now. I hope this helps you towards improving this amazing website even further. :) Thank you for all your work, I really appreciate it.