Does the Bible Speak Negatively About the "World"?

The answer is: it depends on the context. St. Thomas Aquinas clarifies three senses in which the "world" is spoken of in the New Testament:

We should know that “world” is taken in three ways in Scripture. Sometimes, from the point of view of its creation, as when the Evangelist says here, “through him the world was made” (Jn 1:10). Sometimes, from the point of view of its perfection, which it reaches through Christ, as in “God was, in Christ, reconciling the world to himself” (2 Cor 5:19). And sometimes it is taken from the point of view of its perversity, as in “The whole world lies under the power of the evil one” (1 Jn 5:19). (Commentary on the Gospel of John, 1.5.128, trans. Weisheipl)

To summarize, here are the three senses Aquinas clarifies:

World may mean:

1) the created universe, in itself good;

2) the goal towards which creation is culminating, its redemption in Christ, which is also good;

3) the perversity of creation caused by sin, which is under the power of the devil; this is evil.