The application note from ST Microelectronics suggests that the best you can do with this hardware, after tilt compensation, is +/- 2 degrees. http://www.pololu.com/file/0J434/LSM303 ... p-note.pdf
This is not bad for a ~ $30 breakout board.
Here is a much more comprehensive article by a pilot, who also discusses what the professionals do for long range navigation. http://myahrs.wordpress.com/2012/04/20/ ... uld-do-it/
Needless to see, he is pretty emphatic that devices like the LSM303 aren't up to the task of guiding passenger-carrying aircraft.