As much as I love it, I don't think Star Trek in general is such a great place to look for realistic bridge interactions, because they weren't very consistent. If the plot called for someone to make a discovery/perform an action, they would, without much regard for whose job it really was. That said, the new Star Trek movies are a
particularly terrible place to find this stuff, because no attempt was made to approach any level of realism in this regard. It was an action movie. The nanobots are taking over the mainframes and hacking the interwebs, and they're using them to launch a dirty bomb from the moon to melt the polar ice caps.
One more vote for the Harrington series. Even though I don't really care for it, the space travel and combat are very well done. Each bridge officer's role is clear and consistently portrayed, and although the author abuses info dumping to an absurd degree, you end up with a lot of information to draw from. The first book is free, and when I finished that one, the second one was also free, but I don't know if that was a temporary promotion.