You must get all 5 painings. That's when you get the extra trainer star. Talk to the museum curator, and he will give you the glass statue for your secred base.
Also, when using Pokeblocks, not only should you try to max the contest attribute it is participating in, but also the two adjacent attributes. For example, For a cool contest, try and get beauty and tough attributes high also. This will give you a much higher score in the preliminary round.