What periods of the fossil record are most lacking in specimens? What parts of the fossil record are most lacking in specimens? That is, if you were to trace the evolution of a modern mammal (humans, for example) from abiogenesis to now, which periods are the most lacking in fossils? Where are the biggest gaps in our evolutionary history.
The biggest temporal gap would be (IMO) the Precambrian, specifically pre-Ediacarian. Accordingly the biggest gap in the evolutionary history is the origin of eukaryots, both because of the paucity of pre-Ediacarian formations but also because few of the early protists were likely to be fossilizable.  

From the probable apparition of life ca. 3.8-3.5 Ga (e. g. 1 for a review of Archean fossils) to the Ediacarian (ca. 600 Ma) in which metazoans (i. e. "animals") are already diverse (e. g. 2), this is more than 3 Ga of life history for which we have very little fossils (though our knowledge of this fossil record increases currently thanks, in part, to our better understanding of the "chemical" fossil record).

1: J. W. Schopf, 2006. Fossil evidence of Archaean life. Philosophical transactions of the Royal Society, B., 361: 869-885.
2: S.Conway Morris, 1993. The fossil record and the early evolution of the Metazoa. Nature, 361: 219-225.