Beckett is like a teenager. 2:

I guess I'm going to be patient here but I'm bordering on done. You move the relationship along to a certain point. Very far I might add based upon the last episode and then you take 5 steps back. I guess I'll wait until I see it but the four clips suggest the writers are playing with their audience. I'm not impressed.

oh, come on! Castle was just all obsessed with Kyra. Turnabout is fair play. Time for him to get some competition, it's been too long since Will was around. I bet they have a little fight over the newspaper article, or someone talks about the article in a way that makes Beckett realise "she has no life". And she'll go on a date, and Castle will be upset, and thus we'll have progress in the relationship, because we'll get to know that he cares, without going to fast. It's a set up for a lot of fun, from what we've read about this episode.

Clip 2 – I'm just amazed at the level of writing and acting, even just for one simple fun scene like this.

The subtleties in Stana's expressions conveying the embarassment of asking for help getting a date.
And suddenly a glimpse of the passion hidden beneath her usually collected surface, bursting out in "loud". We've seen Beckett being passionate when it comes to solving murder cases, like when she get up close with Castle putting together stories, but this! – Castle would've had a Nikki Heat moment had he witnessed that. And she manages to get from embarrased to passionate so naturally.
Then getting over her embarrasment, she gets a little giddy, smiling with appreciation of nice looking male models. Has me laughing every time (and that's not few).
Writing and acting come together in a perfect mix, creating pearls out of a simple exchange of a phone number.