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I can tend towards being a book snob, so I'm glad I didn't read it first.  As someone who hasn't read the book, I thought it was a good watch.  But as noted, the time dilation issue doesn't really come up in the movie, though it's alluded to at the end.  I just assumed seeing the lady noticeably older was a nod to that, because I'm familiar with the concept from elsewhere.  If I were a casual movie observer who didn't automatically think in those terms, I probably would've wondered what was up with the lady looking older.  It was such a small scene at the end, and there was no explanation, so my wife wondered what was up, and I had to tell her I thought it probably alluded to the time thing which was likely covered more in the book.  Although....utee might remember.....the film may have something about that, somewhere.  If it did, it was quick and probably not something that would clue in the average audience member.

I suspect there was a lot covered extensively in the book that goes pretty fast in the movie.  I probably wouldn't mind that part, though, because just like Lord of the Rings, some things have to be fast-tracked in film to adapt to the medium.  I also suspect it could be very interesting to read the longer process of how Grace learned to communicate with Rocky.  Obviously there's only so much time the film could commit to that. 

I'm actually not sure they addressed time dilation in the movie.  And I have not read the book.

We don't have spoiler tags so now I'm going to put anything that might be a spoiler into the "quoted" text below.  Please ignore it if you don't want to hear specific details about the movie.

The outbound journey was to a place that was just under 12 light years away and they said it would take around 12 years to reach it.  They either stated or suggested that with the powerful astrophage power source, they'd be able to travel near light speed.  But they made no mention of surpassing it.  Then presumably the return journey, either for the probes or for the ship itself, would take another 12 years-- although for some reason I thought I heard when he was about to return to earth, the computer said it would take only 4 years.  But that would require traveling at 3X C, which didn't make sense to me as they never mentioned any kind of warping technology.  Regardless, at 12 years out plus 12 years back, the bare minimum time passage on earth would have been 24 years.  And of course we have no idea how long he and Rocky spent in the Tau Ceti system collecting the samples and developing the solution.  So it's possible that Eva Stratt's increased age was just a result of 24-26 years of elapsed time resulting from the mission itself.  She wasn't exactly "young" when the mission began.  But I'm just speculating here.

One issue with accelerating to near c to visit some star system is what you need to do when you get there, which is SLOW DOWN, somehow.

You could accelerate at a comfortable 1 G and then decelerate at 1 G for a trip of course, you'd need a while (about a year) to get to about 0.9 c.  Then you'd need the same time to decelerate.  You could coast in the interim of course. 

The second issue of course is providing the force necessary to accelerate at 1 G.  There are a few notions as to how, one is the Bussard ram that extracts matter from space around you, then you need a lot of energy to accelerate said matter.  Another is using ground based lasers on a solar sail, but then you need something on the other end that works.

They covered the power source in the book. As utee says, the power source is from the astrophage. 

I barely recall the book, which is perhaps a sign. I agree with utee that in movies, one shouldn't fret over such details.  I do like when a scifi book provides some speculation about stuff.  Clarke was good at that.  

Maybe some day we can make it to a star system somewhere, that would be cool.  One idea is to send a microprobe, which is credible, something quite light that has amazing tech built in for sensing and video.  We're not far from that today.  You'd need a power source of course.  You could hit a solar sail with a powerful laser and get it up to near ligh speed I think.  Twelve plus years later it zooms by the star system, and 12 years later you get data back.  

Then we have the Fermi Paradox which is ... interesting.

Spoiler alert:  don't read this reply to utee's spoiler if you haven't seen it and think you might.

I caught what you mentioned about 12 years there and 4 years back.  So I guess I didn't misunderstand it.  My impression was it was 12 years there from Earth's perspective, but just 4 years from Grace's perspective.  No idea how the math actually works out, but it's true that he would experience less time passage than Earth would.  But if that's what was being alluded to, the movie definitely did not bother to go into any detail, or indeed explain it at all.  

Spoiler alert:  don't read this reply to utee's spoiler if you haven't seen it and think you might.

I caught what you mentioned about 12 years there and 4 years back.  So I guess I didn't misunderstand it.  My impression was it was 12 years there from Earth's perspective, but just 4 years from Grace's perspective.  No idea how the math actually works out, but it's true that he would experience less time passage than Earth would.  But if that's what was being alluded to, the movie definitely did not bother to go into any detail, or indeed explain it at all. 

MORE SPOILERS

Then you caught it. The book delves into that (it was 4 years in Grace time for Grace to arrive there, too).

MORE SPOILERS!

Ah okay.  I didn't catch that, if they discussed it at all.  For the outbound journey I didn't hear them ever talk about the relativistic differences due to time dilation, I only heard them mention the earth-point-of-view which was around ~12 years to travel ~12 light years at near lightspeed.  And of course the return trip should be the same from earth's point of view.  So a minimum of 24 years, plus whatever time was spent in the Tau Ceti system.

 
YET MORE SPOILERS

I don't think they did discuss the difference at all, iirc.  They just said some stuff about it taking ~12 years, and then somewhere else they said something about taking ~4 years to go home, and it was kind of a "Wut?" for me, until the end when they showed the lady significantly older, and I just guessed that the time dilation thing must be what the discrepancy was about.  That aspect of the story, which SF mentioned was integral in the book, was almost entirely glossed over in the movie, as far as I could tell.  

SF would know, having read the book, but I figure it took a long-ass time for Grace and Rocky to figure out how to communicate.  I feel like that part alone would have to be months, if not years.