Below are some comparisons between the predictions of 4 programs / web services in regard to consecutive sunlit ISS lunar transits near Preston, England, the evening of December 4, 2003.  Except for CalSKY, the TLE used was:

1 25544U 98067A   03338.33425327  .00014961  00000-0  18257-3 0  9038
2 25544  51.6276 241.8062 0006209 207.5767 152.5062 15.65278990  7609

The most remarkable thing about these comparisons is that, while CalSKY's predicted path is in good agreement with the other programs, its timing appears to be late by about 21 seconds.

CalSKY apparently used:

1 25544U 98067A   03338.58985813  .00014961  00000-0  18257-3 0  9081
2 25544  51.6309 240.5098 0006233 210.8005 149.2788 15.65208287247640

The discrepancy is evidently due to the fact that CalSKY hasn't yet updated from NASA's Mission Control Center's ISS ephemeris page.

Dec. 4 update: CalSKY is now using the same TLE, and its predictions are now in close agreement with the other programs.

The map below was created from the output of my WorldView program, using Microsoft Streets & Trips 2002. 

B - date
C - time
D - elevation angle of the ISS
E - azimuth angle of the ISS (positive = east from north; negative = west from north)
F - range (miles)
G - latitude for observing the transit
H - longitude
I - how far (miles) can I be from the centerline?
J - is space station sunlit?
K - sun elevation angle
L - sun/moon separation angle

B----- C-----  D--- E----- F--- G------- H-------- I---- J K---- L----
 4 Dec 160320  15.0   97.5  703  53.9033   -2.7361   4.4 y  -2.0 134.7
 4 Dec 160321  15.1   97.6  700  53.9163   -2.5649   4.3 y  -2.1 134.7

Denis Boucher's program:

 Date  Time       RA           Dec         EL AZ  Dist(Min) Range(Km)
 04/12 16:03:20   01h 44m 28s  07d 42m 09s 15 098  5.6m     1124

CalSKY:

16h03m40.91s ISSISS Crosses the disk of Moon. Separation: 0.12d (7.2m) Position Angle: 351.7d
Angular Velocity: 13.1'/s.  Transit duration: 2.00s
Angular diameter: 16.5"  size: 73.0m x 44.5m x 27.5m
Satellite at az:  97.7d E  h: 15.2d  dist: 1122.9 km  mag=0.2m
Satellite apparently moves to direction 261.7°
Centerline →Map: Lon:357d17m46s  Lat: +53d55m53s dist: 3.17 km  az: 352.8d N  Path direction:  82.8d E  ground speed: 11.328 km/s  width: 23.9 km  max. duration: 2.4 s

with up to date TLE:

16h03m20.15s ISSISS Crosses the disk of Moon. Separation: 0.06d (3.6m) Position Angle: 351.9d
Angular Velocity: 13.0'/s.  Transit duration: 2.21s
Angular diameter: 16.5"  size: 73.0m x 44.5m x 27.5m
Satellite at az:  97.6d E  h: 15.1d  dist: 1126.0 km  mag=0.2m
Satellite apparently moves to direction 261.8°
Centerline →Map: Lon:357d17m54s  Lat: +53d55m07s dist: 1.59 km  az: 352.7d N  Path direction:  82.7d E  ground speed: 11.348 km/s  width: 24.0 km  max. duration: 2.3 s

SkyMap:


B----- C-----  D--- E----- F--- G------- H-------- I---- J K---- L----
 4 Dec 173758  28.3  117.7  458  53.9095   -2.7504   2.5 y -14.4 135.4
 4 Dec 173759  28.3  117.8  457  53.8996   -2.6210   2.5 y -14.5 135.4

Denis Boucher's program:

 Date  Time       RA           Dec         EL AZ  Dist(Min) Range(Km)
 04/12 17:37:59   01h 47m 00s  08d 02m 13s 28 118  3.7m      735

CalSKY:

17h38m19.77s ISSISS Crosses the disk of Moon. Separation: 0.03d (1.8m) Position Angle: 339.9d
Angular Velocity: 23.4'/s.  Transit duration: 1.26s
Angular diameter: 25.2"  size: 73.0m x 44.5m x 27.5m
Satellite at az: 117.9d ESE  h: 28.3d  dist: 735.8 km  mag=-0.7m
Satellite apparently moves to direction 249.9°
Centerline →Map: Lon:357d18m12s  Lat: +53d54m26s dist: 0.48 km  az:   7.5d N  Path direction:  97.5d E  ground speed: 8.533 km/s  width: 15.5 km  max. duration: 1.3 s

with up to date TLE:

17h37m58.34s ISSISS Crosses the disk of Moon. Separation: 0.03d (1.8m) Position Angle: 340.0d
Angular Velocity: 23.4'/s.  Transit duration: 1.26s
Angular diameter: 25.2"  size: 73.0m x 44.5m x 27.5m
Satellite at az: 117.8d ESE  h: 28.3d  dist: 736.1 km  mag=-0.7m
Satellite apparently moves to direction 249.9°
Centerline →Map: Lon:357d18m08s  Lat: +53d54m31s dist: 0.48 km  az:   7.4d N  Path direction:  97.4d E  ground speed: 8.537 km/s  width: 15.5 km  max. duration: 1.3 s

SkyMap: