You may have a chance to speak to one or more of the re-enactors, and learn about the authenticity of the clothes he or she wears, the food he or she is eating, and so on. You might meet a British spy, or an officer's wife, as I did. They all have stories, and the character they represent informs their appearance in the re-enactment. If the officer happens to die on the battlefield, I learned, his wife has to find another officer to marry, or she will not be traveling to the next battle re-enactment, as only a certain number can go along.
You might learn that the buttons on a jacket might be authentic, while the cloth they are attached to is a reasonable reproduction. The swords of some of the re-enactors may be authentic, owned by those who fought in battle while those of others are not. In any case, they must have been produced, or represent what was produced, from a time either preceding or of the time of the battle in question. They can't be later models.
If you have a chance to speak and listen to the stories of how the re-enactors got their materials, that alone will be informative. What was the original color of the metal in the sword? How did that change over time? How long did it take to load the guns? Who were the fighters--trained military or local residents? What were some of the strategies and how did they lead to failure or success?
Attending a battle re-enactment is not only informative, but also stimulating. You might end up with more questions than answers, both about how re-enactments are created, and and also about how they reflect historical events.
They are an excellent resource for learning about the history of a place and time from the viewpoint of the individual. The images below are from the bicentennial re-enactment of the Battle of Sackets Harbor in the war of 1812, a re-enactment that was of major historical value and which took place in a beautiful, serene location. The re-enactment could have attracted more interest but seems to have been a pearl viewed by a small and fortunate audience. See the description of the economic and political issues here (NY Times article) :
http://www.nytimes.com/2011/11/25/nyregion/war-of-1812-bicentennial-disorganized-in-new-york-state.html?_r=0
