How secure is the new Mega-site encryption?

The details are relatively scarce, but section 5 of ht developers' page you link to describes the kind of encryption they apply. Bottom-line: they don't say it explicitly, but it is basically CCM mode, albeit with some simplifications in IV management. They don't talk about padding and length encoding, and this might be an issue.

Also, the file is split into chunks, each chunk having its own MAC, so that you may "process" chunks individually. However, it seems that there is no sequence number in the MAC thing; as far as the text says, the IV for the MAC of the second chunk is the CBC-MAC of the first chunk, which is bad because it could be altered by a malicious individual. In practice, this means that the per-chunk MAC is useful only if you stream the data from the beginning, in due order; random access would be susceptible to attacks.

The main concept of using a per-file key is sound, but it requires some careful handling of the keys and there is not enough detail on the page to decide whether things were done properly or not. The whole thing reeks of a homemade construction and it is known that homemade constructions are fertile ground for vulnerabilities.