I should note that the Bible Society report for 1858 says that the Bibles were not revised, but carefully collated according to the best editions.
One difference that can be found between an ABS 1845 Bible and one from 1851 is changing from "Cherubims" to "Cherubim" in Genesis 3:24. However, this did not change back. It shows up in editions I have from 1884 to 1903 (all downloaded from Google books).
The entry in Darlow and Moule (see previous post for a copy of this) says "Some fruit, however, of the collator's careful work remains in the later editions published by the A.B.S., which are generally commended for their accuracy." Now, to find some examples of fruit that didn't remain!
One such change is in Jude 1:11 where "Core" was changed to "Korah." This appears in editions from 1853 to 1859. Editions from 1884 on (those found on Google) have gone back to "Core." Obviously, this isn't a theology modifying change, but does help identify Bibles in the ABS editions.
I should also note that Scrivener discusses the A.B.S. work in his book The Authorized Edition of the English Bible (1611): Its Subsequent Reprints and Modern Representatives on pages 36 through 39.