I found that this happens when resizing a large logo, i.e., a white circle on transparent bg, from 600px to 68px. I recreated the problem and took screenshots.
Is something not working like it should? Let us know.
As a workaround, I do my resizing in Preview.
Thanks for the bug report — we've reproduced this and it happens due to the resizing algorithm that Pixelmator uses. We chose that algorithm specifically because it produces fewer artifacts and features better quality when resizing photographic images but the trade-off is that it's not the best for dramatically reducing geometric shapes like this. We'll see what we can do to improve this in the future, though.
Thanks for the reply! Yep, creating very small icons is a fairly specific task.