We can state for sure only several grammar traits of Common Anatolian. Four noun cases had flexions practically the same as in Proto-Indo-European. There were only 2 genders: common and neuter, and this is really unique, because it reflects the stage of the Proto-language when animate and unanimate things were the only distinction, no masculine and feminine opposition.
The verb system consisted of two moods (indicative and imperative), two tenses (present and preterite), two voices (active and medium). But verbal endings are very strange for they have few correspondences in Proto-Indo-European or other Indo-European languages. The -hn / -n ending of the 1st person preterite is not found anywhere else except Anatolian languages; the same can be said about -weni, -meni (1st person plural), -lu (1st person singular of imperative).
Common Anatolian is a highly archaic tongue, with lots of traits derived directly from the ergative (early) stage of Proto-Indo-European. And this was inherited by later Anatolian branches - Hittite, Luwian, Palaic.