I'm not sure what is my favorite episode... I have a so many favorite scenes! But I think if I had to pick only one episode to watch from season 1 - I'd pick the season finale. I thought that was a good moment there, at the end when Castle has to tell Kate he's found something with her mother's case.
I also thought it was so funny when Kate shows up at his book reading in that hot pink dress! ;) I don't remember the name of that episode!
Oh I love season one and I love the pilot, the very first time we see them together. Kate all nervous trying to pretend that she hate him. LOL Priceless moment!
For my Season 1 favorite episode I would probably have to say 1x05. Maybe because that is really the first episode I watched! I also really liked the season finale. :)