Why is second pKa value of phosphoric acid different across different sources?
Someone will probably come along and move this to "chemistry", but here goes anyway.

The answer is: it depends upon how you measure it.

See:


  Jungas, RL (2006) Best literature values for the pK of carbonic and phosphoric acid under physiological conditions. Analytical Biochemistry 349 1-15


The author states that   "..the best value for the true thermodynamic second dissociation constant of phosphoric acid in pure water at 38&deg;C is 7.180, rounded to the nearest 0.005." 

He then goes on to re-analyse the data reported in:


  Cohn, EJ (1927) The activity coefficients of the ions in certain phosphate solutions: a contribution to the theory of buffer action. J Am Chem. Soc. 49 173-193


and concludes that under physiological conditions of ionic strength and pH the best estimate is 6.795.