The anecdotal history note is interesting but I suggest a more factual note be included. For example the paper [P. Stoica and B. Ottersten, The evil of superefficiency. Signal Processing, Vol. 55, pp 133-136, 1996] makes the following remark on the history of the CRB: "As an historical aside we remark on the fact that what is now known as the CRB inequality was apparently discovered, for the single-parameter case, by Doob  and rediscovered in a neater manner by Frechet [ 6]. Darmois , Cramer [ 3] and Rao [ 8] have presented generalizations of the CRB inequality to the multi-parameter case. In particular the CRB derivation by Cramer in  is a masterpiece that is worth reading even nowadays." All the above references may be cited explicitly in the current note.
There are at least two additonal extensions of the CRB that are worth mentioning: the CRB for biased estimates (I think VanTrees book is a good reference for this CRB) and the CRB for constrained estimates, see e.g. the paper [P. Stoica and B. Ng, On the Cramer-Rao bound under parametric constraints. Signal Processing Lett., vol 5, 177-179, 1998] and the references therein.