Many new Saturnian moons are now confirmed; the pre-2000 reports are probably in error. Here is more up to date data. More recent discoveries can be seen here
          S/2000 S 1
          S/2000 S 2
          S/2000 S 3
          S/2000 S 4
          S/2000 S 5
          S/2000 S 6
if confirmed they will be assigned permanent names.
          S/2000 S 7
          S/2000 S 8
          S/2000 S 9
          S/2000 S 10
          S/2000 S 11
          S/2000 S 12
  
                       Distance
          Designation    (km)
          -----------  --------
          S/1981 S 7
          S/1981 S 10
          S/1981 S 11
          S/1981 S 14   200000?
          
          S/1981 S 15   174000
          S/1981 S 16   220000
          S/1981 S 17   231000
          S/1981 S 18   185000
          S/1981 S 19   186000
          
          S/1995 S 1    137450
          S/1995 S 2    139700
          S/1995 S 3    141050
          S/1995 S 4    146450
          S/1995 S 5    140060
          S/1995 S 6    139910
          S/1995 S 7    139440
      The first two groups are derived from analysis of
      Voyager 2 data reported in 
      IAUC 6162;
      the third group is from
      HST observations
      during the May 1995
      ring plane crossing
      by Amanda S. Bosh and graduate student Andrew S. Rivkin and reported in 
      IAUC 6192;
      the fourth group is from HST observations by P. D. Nicholson et al
      during the August 1995 ring plane crossing as reported in
      IAUC 6243.