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In the first part of this paper, we discuss the notion of irreducibility ofcycles in the moduli spaces of n-marked rational tropical curves. We prove thatPsi-classes and vital divisors are irreducible, and that locally irreducibledivisors are also globally irreducible for n \leq 6. In the second part of thepaper, we show that the locus of point configurations in (\R^2)^n in specialposition for counting rational plane curves (defined in two different ways) canbe given the structure a tropical cycle of codimension 1. In addition, wecompute explicitly the weights of this cycle.

Irreducible cycles and points in special position in moduli spaces for tropical curves