The mutation rate in eucaryotes is generally 109. This means that there are about three point mutations per generation. Nearly all of these will be in non-coding, probably "meaningless" regions of the genome. Any new mutation is heterozygous in one parent. For a mutation to be fixed, two offspring need to get the mutation from that parent, and be chosen for further breeding. In the F2 generation, only one quarter of the offspring will then be homozygous, and two homozygous offspring need to be mated in F3 for the mutation to become finally fixed. Therefore, the different substrains of inbred mouse lines, for example C57BL/6NTac vs. C57BL/6J, will differ only slightly from each other and from the common ancestor. There will be actually less change than in outbred lines with small breeder populations. It will be very difficult to find any "meaningful" point mutations that distinguish two substrains etc., short of sequencing two substrains.

Microsatellites (repeat sequences like CACACACA...) are a different story. The mutation rate is much higher, 10-2 to 10-5 (literature data vary widely, this also seems to depend on the length of the repeat). Taconic looked at the microsatellites in five inbred strains, among them C57BL/6NTac and C57BL/6J. We found that of 342 microsatellites tested, only 12 were different between the two substrains. The substrains were separate for at least 150 generations. From that data one could make a highly speculative calculation: in 34200 microsatellites there would be 1200 variations. If the mutation rate in genes (see above) is approximately one million-fold lower than in microsatellites, and genes are approximately one thousand-fold larger than microsatellites, one would expect one "meaningful" mutation to have occurred in 30000 genes of the mouse during those 150 generations, so that every substrain is different in 1 to 2 genes from any other substrain.

Therefore, one can never be 100 percent sure whether a point mutation did occur in a certain substrain. There is indeed anecdotal evidence that some B6 substrains are more susceptible to skin lesions than others, which could be due to a point mutation somewhere in the line. For a dutch substrain, C57BL/6JNmg, there is detailed data on differences in behavior and neuroanatomy compared to C57BL/6J (Pager J, Mineur YS, Pinoteau W, LeRoy I, Crusio WE.(2001): Neuroanatomy of cerebellum and olfactory bulb in a substrain of C57BL/6J inbred mice carrying a spontaneous mutation. Physiol Behav 73:827-31; and earlier papers by W. E. Crusio's group)

The best way to avoid any problems with mutations would be to cryopreserve a large number of embryos from each strain and go back to that repository every 20 generations or so. This way, the strain would be "frozen in time." (Gerald W. Bothe, Taconic Biotechnology)

References
C57Bl/6j Information