Gosh, I'm definitely not seeing the scene in the Transporter room the same way as you all. Surprise surprise right...
This day was like the day without end.....so much action and drama taking place on their
first day on the job...As far as the Transporter room, I didn't see it as desperate on Uhura's part...I didn't see it as this is what she would do every time Spock transported,
but for a first day on the job..to see your partner/bfriend/lover's PLANET collapse upon itself into nothingness...to know his Mother just died, AND to know that he was/is the designer of the Kobayashi Maru(no win situations) I would think any intelligent woman would know this wasn't just a simple mission that he would be coming back from...and truly had Scotty not transported when he did..Spock would not be back...I can cut her some slack.
I don't believe Kirk had been in the job long enough to be embarrassed by S/U's action ---I think he was surprised just like the rest of us.. he was more interested in the fact that the conversation they had was more mature than lover's lies he's probably whispered in many a female's ear... and the fact that he actually heard what he thinks is her first name...he never put them together as a couple..and if he was shocked at anything, I would think it would be that Spock and Uhura were a couple...not that they were being unprofessional in front of their Captain...
Scotty and his assistant (who now run the ship's transporter room as the most reliable source for gossip) couldn't possibly have heard anything that was said by U/S and I actually thought Simon Peggs over dramatic eye lift was over the top and un necessary...what does it matter to him...what does it matter to any one on this freaking HUGE StarShip...there are probably a hundred other relationships going on with the crew...No one knows...even when they were safely transported back..Spock runs to Uhura or they run into each other, but they do not hug and I thought they should have...they sort of run into each other with their hands raised before the camera cuts away.
Franklin I was joking ...you were joking...we're all cool!
ciao for now
goodness, I've gotten way behind on this thread! so many responses to catch up with, but in any case I'm of the opinion that there is more criticism of the transporter scene than it really warrants. I do doubt that many new Star Trek fans are having the same issue with it. Now, I started watching Trek in the 70's in syndication, so do I understand the surprise and discomfort some feel, but I don't mind a bit if Spock's character evolves along a different path. I'm not wedded to his first incarnation and I feel the writers had a sense of respect for the tradition while moving forward, taking some chances and doing what they felt would work for this current iteration.
I don't think they intend to transform him into someone we don't recognize.
As I see it the turbolift scene and the transporter scene have different purposes. On the turbolift we're introduced to the fact that there is a relationship or a growing relationship. He accepts the kisses and comforting and you know that he wants them/appreciates them, but Spock is more or less impassive ( or maybe he's in a state of shock as well) and he pulls her off and restarts the turbolift.
In the transporter scene Spock is different. This takes place after his father has revealed to him that he married his mother because he loved her. Now we see a Spock who is fully reciprocating with loving eyes and soft tone of voice. I can't remember the exact dialogue. (Oh well, I'll just have to see it a few more times and give Paramount some more of my money.

) These are two people who love each other and Spock accepts his feelings and isn't hesitant or holding them back. And I think this is meaningful...Spock feels permission to love this woman. And why shouldn't Spock be allowed to love? He's allowed friendship.
Maybe it's surprising that they'd have this loving communication in public, but under the circumstances it is completely understandable as others have pointed out. I also feel that it was quiet, heartfelt and not over-the-top. As well as fellow crew members these characters are a family-and they are going to know each others business and be involved with each other and come to know each other very well. That's all to the good from a dramatic standpoint, I think. I don't know what Starfleet protocol is and I don't give a crap. I hope characters break it whenever appropriate

I'm kind of wondering if some people are using the current military as a guideline for what Star Fleet is? I don't really think it's exactly the same.
Another aspect to this transporter scene is that Spock isn't trying to hide their relationship anymore. He's not going to get into the details with Kirk at this point, but he doesn't care who knows, now. And that's kind of validating and affirming of their relationship, really.
I also wouldn't exactly use the word desperate to describe Uhura. Like yourself, I'm new around here so I don't know people or where they all are from

, but it occurs to me that it could be due in part to a slighly different connotation of the word in US/UK/other English? Usually I'd think of using the word desperate for someone who is far more grasping and aggitated than she displayed. And as such it has a somewhat pejorative sense to me.
Lastly I wanted to add that I just think the Spock/Uhura scenes were very beautiful, touching. I wouldn't be surprised if they were even moreso that JJ or Orci and Kurtzman thought they would be. The actors really worked well together and especially giving a nod to Saldana there. And Quinto has a certain intensity that gives it a feeling of depth as well. They really have something with this imo, and I hope they use it well.