Is it permissible to place small statues for decoration, and is it permissible to listen to a recorded Qur'an on a CD with incomplete verses?

It is not permissible to place statues in the home for decoration or otherwise. As for an incomplete Mushaf, it is preferable to complete what is missing from it or replace it. If that is not possible, and there is a concern that some might mistakenly believe it to be complete, then it must be disposed of in a manner that preserves its sanctity, such as burying it in a pure place, similar to a Mushaf that is no longer used, and a believer who is buried as a sign of honor.