The Gemarah (Rosh Hashanah 34b) says that pausing during Hallel might invalidate one's recitation. Presumably (though maybe not) talking during Hallel is also problematic. May one speak during the ...
On a day when Hallel is recited (for example Rosh Chodesh) I've heard that one should not (lichatchila) speak between Shemoneh Esrei and Hallel. Rather, as soon as the chazzon finishes chazaras ...