My three word review of the movie was: Brad Pitt Speaks
With respect to science, a Flat Earth Society meeting has more accurate science than this movie.
Spoilers, so if you want to go see it, stop now!
The antenna tower is unrealistic and doesn't really offer any significant advantage to terrestrial antenna farms
The moon buggys seems to have pneumatic tires. Also, if you had to go to the far side, why go on the surface. Take a smaller flying craft. It could be hundreds if not a thousand or more miles to get there.
We figured out that you don't land the entire craft on the planet during the Apollo program. But the ship going to Mars lands upright and intact? If they just want his voice for the "secure laser" why not just have him record it on Earth and take the recordings to Mars. It's a lot less costly to send less than a kg of recordings than 80kg of astronaut, plus everything needed to keep him alive. Plus you have control over the message so he doesn't ad lib.
Getting on the craft as it's leaving for Neptune, yeah right!
The grand tour of the planets. Odds are they are not in a line and since this was supposedly in the "near future" as stated in the opening of the movie, there is likely not going to be another alignment of the planets for a grand tour like the Voyager program for about 100 years. So he wouldn't go past every planet on the way to Neptune.
Why park your ship in such a different orbit from the craft you are planning to board?
If the anit-matter needs to be contained to save the solar system, how exactly does a nuclear detonation accomplish this?
Even if the rotating antenna could fling you to your craft in a different orbit, your flimsy shield is not going to protect you from orbiting bits of ring traveling at 10's of thousands of kph.
The nuclear detonation is not going to send you 3 billion miles home.
Exploding space monkeys, not really!