We describe some implications for massive dihadron production experiments of recent observations in Fermilab experiments E609 and E557 of large nuclear rescattering effects in dijet production in hard pA collisions. Substantial upward corrections to a (in the A a cross section parametrization) are indicated for dihadron experiments which detect symmetric back-to-back hadrons with narrow acceptance in azimuth or pr. Other consequences of the large nuclear rescattering are also discussed.PACS numbers: 25.40.Ve, 13.85.Ni, 24.85.+p It has been realized for many years that a nucleus can serve as a valuable "laboratory" for experimental study of the scattering and hadronization of high energy quarks and gluons. In this Letter, we shall consider experiments which have used nuclear targets to study hard scattering reactions such as Drell-Yan dilepton production, dijet production, and dihadron production. For these reactions, perturbative QCD now provides a well-understood, experimentally established framework for describing the basic hard scattering process. Nuclear effects can be observed as changes in the properties of hard scattering events compared to scattering from a free-nucleon target.Experiments [1,2] have shown that nuclear effects are quite small for Drell-Yan dilepton production in hadronnucleus collisions. The measured kr (the rms value of the magnitude of the transverse momentum vector) of the dilepton system produced from a free-nucleon target is typically [3] about 1.4 GeV/c. This kj represents the combined effects of intrinsic transverse momentum (confinement) and initial-state gluon emission. For Drell-Yan dilepton production using heavy nuclear targets rather than a nucleon target, it was found that kr hardly changed by a detectable amount [1,2], implying that the initial-state parton had experienced very little nuclear scattering. The measured nuclear contribution to kj was about 0.4 GeV/c.More recently, in Fermilab experiment E609 [4], a drastically different situation was found for dijet production in pA collisions at 400 GeV/c. The nuclear contribution to kr, where kr is now the rms net transverse momentum of the final-state dijet system, was measured to be about 2.5 GeV/c. Similar very large nuclear kr effects are also evident in the dijet data of Fermilab experiment E557 [5] at 800 GeV/c. A straightforward interpretation of the above experimental results is that parton hard scatterings within nuclei involve very little nuclear scattering of the incident parton, but that there is substantial nuclear rescattering of outgoing hard scattered partons. Such an asymmetry between initial-state and final-state nuclear scattering may be related to the so-called Landau-Pomeranchuk effect [6,7]: Initial-state soft gluon radiation within the nucleus will be strongly suppressed because of the smallness of the proper time which is available between an initial-state nuclear scattering and the hard scattering.These two phenomena, the large value of kr (nuclear) for dijets and the fact that the nuclear rescatte...