The latest version of Clippy introduced some new lints, and will now
complain about the deprecated syntax. Unfortunately, the new tool_lints
syntax doesn't work on older Rust versions so we can not yet start
using it.

This commit also refactors various disabled Clippy lints away. Some of
the disable lines are still necessary as Clippy is overly pedantic, but
this at least gets rid of a large portion of them.