This movie was working toward two goals: to make a political point and to tell a scary adventure story. It's often difficult to do make a political point and still tell a good story (consider the highly political but rarely-entertaining final season of Ellen). Beyond Rangoon finds a good balance between politics and storytelling.
I already knew that Aung San Suu Kyi had won the 1991 Nobel Peace Prize, and knew something about the oppressive political situation in Burma, so the political message of the movie was mostly a dramatization of what I already knew. But I thought the movie did a good job of telling about Aung San Suu Kyi and the mostly-faceless dictators who have for years tried to silence her. The device of presenting an unfamiliar setting through the eyes of a character that viewers can identify with is fairly common, but it's quite well done in this movie.
Of course, the real measure of the movie was its entertainment value. Arquette was excellent as a young woman whose sister took her to a distant, unfamiliar place to shake her out of her depression over the violent deaths of her husband and son. She is convincingly detached and depressed. Her grieving condition gives her a clear reason for her distracted wanderings into the thick of a dangerous situation she does not understand, something she'd otherwise be much too intelligent to stumble into.
Once the dangers become so obvious that she can see through them even through the cloud of grief, she's trapped, with no easy escape. That sets her on a path of adventure where she needs her intelligence to survive. The writers deserve much credit for making her intelligent and resourceful enough to deal with numerous dangerous situations, while still finding a plausible reason for her to be foolish enough to get into trouble in the first place. The directing is strong also, keeping up the tension throughout the race to escape the forces of the dictatorship.
This movie had additional impact on me and my wife because of other events of the same time period. We were preparing for a trip to India, and heard news reports of Western tourists who had been taken hostage by a terrorist group in India. Avoiding isolated terrorists in a peaceful democratic country is quite a different matter from escaping an oppressive dictatorship. But the movie and the news shared the element of avoiding danger in an unfamiliar country. That common characteristic gave the movie meaning beyond the strength of its own skillful storytelling. The movie illustrates the international tourist's worst nightmare.