subscriber: fix broken docs links (tokio-rs#1902)

This branch fixes some broken documentation links and other docs issues
in `tracing-subscriber`.

tracing-subscriber/src/lib.rs

@@ -64,6 +64,8 @@
 //! - `local-time`: Enables local time formatting when using the [`time`
 //!   crate]'s timestamp formatters with the `fmt` subscriber.
 //!
+//! [`registry`]: mod@registry
+//!
 //! ### Optional Dependencies
 //!
 //! - [`tracing-log`]: Enables better formatting for events emitted by `log`
@@ -81,7 +83,7 @@
 //! used without requiring the Rust standard library, although some features are
 //! disabled. Although most of the APIs provided by `tracing-subscriber`, such
 //! as [`fmt`] and [`EnvFilter`], require the standard library, some
-//! functionality, such as the [`Subscribe`] trait, can still be used in
+//! functionality, such as the [`Layer`] trait, can still be used in
 //! `no_std` environments.
 //!
 //! The dependency on the standard library is controlled by two crate feature
@@ -158,6 +160,7 @@
 //! [`env_logger` crate]: https://crates.io/crates/env_logger
 //! [`parking_lot`]: https://crates.io/crates/parking_lot
 //! [`time` crate]: https://crates.io/crates/time
+//! [`libstd`]: https://doc.rust-lang.org/std/index.html
 //! [`liballoc`]: https://doc.rust-lang.org/alloc/index.html
 //! [`libstd`]: https://doc.rust-lang.org/std/index.html
 #![doc(