Analyses of the J/ψπ[superscript +]π[superscript -] decay channel of the X(3872) resonance by the CDF, Belle, and LHCb Collaborations have established its J[superscript PC] quantum numbers as 1[superscript ++]. An analysis of the π[superscript +]π[superscript -]π[superscript 0] invariant mass distribution in the J/ψπ[superscript +]π[superscript -]π[superscript 0] decay channel by the BABAR Collaboration indicated a preference for 2[superscript -+] over 1[superscript ++]. We point out that a proper evaluation of the χ[superscript 2] in that analysis increases the probability for 1[superscript ++] from 7.1% to about 18.7%. In the case of quantum numbers 1[superscript ++], where the X has an S-wave coupling to J/ψω, the proximity of the J/ψω threshold to D[superscript *]D̅ thresholds and the narrow width of the ω suggest that the effects of scattering between J/ψω and charm meson pairs could be significant. We derive invariant mass distributions for J/ψπ[superscript +]π[superscript -]π[superscript 0] and π[superscript +]π[superscript -]π[superscript 0] that take into account S-wave scattering between the D[superscript *0]D̅[superscript 0], D[superscript *+]D[superscript -], and J/ψω channels. We also analyze the effects of scattering through the χ[subscript c1](2P) charmonium resonance. We find that scattering effects are unable to produce significant changes in the shape of the π[superscript +]π[superscript -]π[superscript 0] invariant mass distribution.United States. Dept. of Energy (Grant DE-FG02-91-ER40690)United States. Dept. of Energy (Contract DE-FG02-94ER40818)