ESPN's Stats and Info team looked at the average scoring margin of the five games in the book in the 2011 NBA Finals between the Miami Heat and Dallas Mavericks in comparison to other playoff series since 2003 (when play-by-play data became widely available). The Finals have been the second closest series in that span, with an averaging scoring margin at any given second in any given game in the series being 3.62 points. Only the 2007 Eastern Conference Finals between the Detroit Pistons and Cleveland Cavaliers (starring, of course, LeBron James) has been closer, with an average margin of 3.34.
When you account for the margin of games won to games lost to give long, competitive series a boost, this series is third, behind the 2007 ECF and 2009's battle between the Chicago Bulls and Boston Celtics that saw tons of overtime.
The Stats and Info group found that the average score margin for all playoff games since 2003 is 7.44 points. The highest average score margin for any of the Finals games in this series is 4.89 in Game 3, where the Heat led by 14 late but won by just two.