Lucid Food: Cooking for an Eco-Conscious Life is the first library ebook that I checked out on my Kindle. The checkout process was smooth.
The only thing that is different is that you have to download via wi-fi vs. 3G. Amazon does not let you use 3G for library books. A friend has a Kindle 2 that does not have wi-fi. It has 3G only. To get library books on their Kindle they have to download the file and move it via USB to the Kindle. Not that big a deal but a step that needs to be done.
All the new Kindles have wi-fi so this will not be an issue for anyone that got a Kindle recently.