This is Star Trek dealing with the issues of its day, and here that issue is racism. In retrospect it's not exactly subtle about it (Stiles' bigotry makes that kind of difficult) but I do remember, when I first saw it, the shock at seeing the Romulan commander for the first time, that he looked like Spock, that it called into question everything about a member of our crew. With the show in its infancy at the time it was something of a masterstroke.
There are some nice contrasts in this episode (the wedding in the middle of such a taut situation, for instance) but it is the similarities between Kirk and his foe that stand out. The best enemies are the ones that are equal to or better than our hero (which is what made Khan such a success later on) and Mark Lenard did a fantastic job of conveying his character's quiet convictions. The quiet moment between Kirk and McCoy is also very well done.
The final scene in the Enterprise chapel sticks in the memory - the way Kirk gazes at the cross before turning and walking out - a good reminder of how great the show was before 60s cheese took over.