I think Eigenbunny's explanation cuts to the heart of the matter. Here are some more specific details in the case of symplectic field theory.

First of all, to get some intuition for what bad orbits look like, in the case of a 3 dimensional contact manifold, the bad orbits are precisely the hyperbolic orbits that have non-orientable stable and unstable manifolds. For simplicity, I will talk about cylinders, but the general case is very similar.

(1) The bad orbits must be thrown out because of an orientation problem. In SFT, the simple orbits are decorated with a choice of marked points on each one, called markers. Also, the domain curves are decorated with *asymptotic markers*. These are a choice of marked point in the circle at infinity for each of the cylindrical ends of the domain. Now consider a holomorphic half-cylinder asymptotic to the $m$-fold cover of a simple orbit $\gamma$. By the convergence result, the image of the asymptotic marker makes sense, and is a point on $\gamma$. We want the image of the asymptotic marker to match the marker on the orbit. Given an unmarked curve, we have $m$ possible locations for the asymptotic marker on the domain.

To understand how to glue, we want to think of how a level 2 building can arise as the limit of cylinders. Suppose we break at the $m$-fold cover of $\gamma$. The two ends asymptotic to this orbit don't obtain an asymptotic marker -- only a marker relative to each other. We can think of this as having $m$ possible choices of asymptotic marker on each end, and then identifying the ones obtained by a simultaneous rotation, giving us $m$ possible choices in the end. Now, for us to count these curves, we need the rotation of the markers to consistent with the orientations. In general it is, but for bad orbits, this is orientation reversing.

This business with markers is one of the places where we see the equivariant nature of SFT: we break the $S^1$ symmetry with these markers, and then quotient out by all possible choices to remove the dependence.

For more details, Bourgeois and Mohnke's Coherent orientations in symplectic field theory does a good job explaining this in detail. Also, see the Introduction to SFT paper by Eliashberg, Givental & Hofer (Section 1.8.4 and Remarks 1.9.2, 1.9.6)

(2) This is also because of the $\mathbb Z_m$ action. Consider the simplest example, where we look at the boundary of a 1-dimensional moduli space of cylinders connecting orbits a and a'. (By this, I mean 1 dimensional after the quotient by the translation.) Suppose one boundary component consists of a level 2 building with two cylinders, a to b and b to a', and b is a bad orbit. Suppose b has multiplicity $m=2k$. Then, the boundary building has $m$ different possible decorations by asymptotic markers. If you chase through the orientations, the end result is that these terms all cancel out, thus saving us from having problems with $d^2$.

(3) The answer to the most optimistic version of this question is no: here is no reason for the moduli space to be empty in general. In order to get a signed count of zero, one needs to make sense of orientations. The way orientations are done in SFT, these moduli spaces asymptotic to bad orbits don't even get one, so the signed count doesn't make sense. Arguably, this isn't the only way we might define orientations (to get the same theory). A related situation in which something like this is true is in the isomorphism between linearized contact homology and $S^1$-equivariant symplectic homology (actually the $SH^+$ part), due to Bourgeois and Oancea. Their non-equivariant contact homology involves decorating each Reeb orbit with a Morse function and imposing markers. The ``bad'' orbits end up dying (over $\mathbb Q$) because the differential of the maximum, instead of being $0$, is then twice the minimum.