The nano update, which is version 1.0.3, fixes several issues including instability when using the Nike + iPod Sport Kit and a problem that caused Cover Flow art to be distorted after playing a slideshow with TV out. Apple also fixed a problem that caused photos to be distorted when waking the nano from sleep.
Support has been added to the nano for Apple's new earphones and in-ear headphones with remote and mic. A setting has been added to turn off Cover Flow when rotating the nano.
The iPod classic update, which takes the software to version 2.0.1, also added support for Apple's new earphones and in-ear headphones with remote and mic, as well as fixing a bug with saving Genius playlists.
Both updates are available through iTunes when your iPod is plugged in.