There is one place that really made me think they'd forgotten about the comm latency: when Mark asks about the crew's reaction to the news he's alive, he sends "RU receiving?" after he doesn't get a reply. This seems like something you'd do only if communication was real-time.
But if you watch the scene carefully (which apparently I didn't the first time), you can see that he was sitting back in his chair, and only sent that after looking at another screen to his side (presumably with a clock). They do a decent job of showing that he had been waiting a while (for the expected comm round-trip time), and didn't still have his hands on the keyboard like you would after a 10 second pause.
After Kapoor sends "we haven't told the crew...", he starts to stand up from his computer before the shot cuts away. Presumably he's going to get a drink or something while waiting for the reply, since obviously there is lots more to talk about with Mark (on other subjects).
When the reply does come, people are standing around the office like they're waiting.
So there are subtle visual cues about the time jumps in each cut between send and receive.
Having the conversation "broadcast live all over the world" is a little weird. It's not plausible that TV news stations would just show it continuously with at least 20 minutes between messages. TV and radio news would have to cut back to it for every update, which would let them take an extra couple seconds to screen it for profanity. Presumably they just meant that it's going up live on NASA's web site as it comes in.
In the commentary track for that scene, they address it directly:
Weir (author of the book): I also really appreciate you guys maintaining the communication latency. As far as I can tell, that is the hardest thing for Hollywood to do...
Goddard interjects: It's really hard.
Weir: ... is accept the fact that there's a communication latency.
Goddard (author of the screenplay): I guess it does sort of go against the nature of cinema. 'Cause you cut between one place to another and in your mind it doesn't quite make sense.
Weir: This one bit right here where he doesn't get an immediate response, so he's like "Are you receiving?". I'm like, "Well, technically he would have been waiting 20 minutes."
Goddard: All right. Let's no-prize it. He waited 20 minutes, the normal amount of time.
Weir: And there was no immediate response. And so he's like "Hey."
Goddard (joking): That's right. We shot those 20 minutes, but it was boring.
Weir: Yeah, right. You just pointed the cameras at the actors and said ...
Goddard: "Now just wait".
The three different methods of communication shown in The Martian
Answer yes/no questions by pointing the camera. Pretty terrible for proposing new ideas to Mark: No way for NASA to tell him what yes/no question to ask. Also tricky to have multiple questions in-flight because you'll get mixed up on which yes/no went with which question.
Mark->Earth: messages on boards. NASA->Mars: ASCII transmitted 4 bits at a time (hex digits as symbols). Same latency (well, higher if you include decode time), much higher bandwidth. Mark can receive messages without a round-trip to Earth. But only when standing outside watching the camera move.
Two way text (and presumably data, like email attachments). Fully asynchronous. NASA can send stuff while Mark is busy doing something else, and he can see it when he next checks the screen. Same latency, vastly higher bandwidth.
They all have the same latency (+/- manual decoding time), but there are huge increases in bandwidth with each revision. The first one is so limited that the second one (manually-decoded ASCII) is a qualitative change, not just a quantitative bandwidth improvement.
The third communication method (fully computerized) should make it much easier to deal with the large delay * bandwidth product. Multiple whole messages can be "in flight" at once in each direction.
If you've ever had a text-chat conversation with someone where you're still replying to an old message while they're starting to say something new, imagine that. You will have multiple topics of conversation happening in parallel.
Ideally each conversation in separate windows on screen. Or set it up like email, with a different thread for each topic.
(Initial contact would be something simple hacked together like shown; a threaded chat program would come later).
So instead of sitting there waiting for a reply to your last message, you'd go eat something, or alt+tab and reply to a different message. You'd be talking to botanists about your plants, talking to habitat engineers about any maintenance issues, talking to a doctor about your health, etc. etc.
It's easy to imagine that this is "what happened", even though the movie doesn't explicitly show it. Movies rarely have time for the interesting details of a lot of things.
The other thing that seemed odd was that messages appear on the receiving screen at about typing speed. Communication over that distance results in very weak signals on the receiving end, so sending a single character reliably would actually require sending a whole data packet with error-detection and correction codes. (See this short article about NASA's Deep Space Network.)
Given that the minimum round-trip time is over 3 minutes, composing a whole message and sending it would not add a significant amount of extra delay, and would make more sense (and probably would have been easier for the engineers to implement).
I guess there's plenty of bandwidth to send a whole packet for each character if we're only talking about human typing speed, though. There's no technical obstacle to implementing it that way.