NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. In this work, we describe three analyses, all of which involve physics beyond the Standard Model. The first two discussed here are closely related; they use effective operator analyses to constrain the contributions of physics beyond the SM to observable processes. The third project involves the investigations of a particular extra-dimensions model which addresses the cosmological constant problem. The first project which we will discuss uses the scale of neutrino mass to place model-independent constraints on the coefficients of the chirality-changing terms in the muon decay Lagrangian. We list all of the dimension-six effective operators which contribute to muon decay and Dirac mass for the neutrino. We then calculate the one-loop contributions that each of these operators makes to neutrino mass. Taking a generic element of the neutrino mass matrix to be of order [...] 1 eV, we derive limits on the contributions of these operators to the muon Michel parameters which are approximately four orders of magnitude more stringent than the current experimental results, and well below near-future experimental sensitivity. We also find two chirality-changing operators, which, due to their flavor structure, are unconstrained by neutrino mass yet contribute to muon decay. However, as these two operators differ from those constrained by neutrino mass only by their flavor indices, we naively expect their contributions to also be small; if their effects instead turn out to be observable, this may be an indication of beyond-the-Standard-Model physics with an interesting flavor structure. In the second analysis, we again perform an effective operator analysis, this time applied to Higgs production at a linear collider. Here we include all dimension-six operators containing fermions which contribute to Higgs production. We again include operators that contain right-handed Dirac neutrinos. We obtain limits on these operators from electroweak precision observables, the scale of neutrino mass, and limits on neutrino magnetic moments, and use these limits to constrain the contributions of these operators to the Higgs production cross-section. Although we find that all operators containing right-handed neutrinos contribute negligibly to Higgs production, we do find three operators containing only SM fields which could have observable contributions at an [...] linear collider. Lastly, we discuss the characteristics of a particular extra-dimensions model originally proposed by Carroll and Guica . This model has two extra dimensions compactified into a sphere, a bulk magnetic field, and a bulk cosmological constant. In this model, the cosmological constant seen by a four-dimensional observer can be set to zero by fine-tuning the bulk magnetic field against the bulk cosmological constant. If branes with a tension are added at each of the poles of the two-sphere, solutions with zero four-dimensional cosmological constant are still possible, but the compactified dimensions must acquire a deficit angle which depends on the brane tension. However, the brane tension does not affect the fine-tuning relationship between the bulk cosmological constant and the bulk magnetic field. This feature led to the hope that, after this fine-tuning, the model might self-tune, keeping the four-dimensional cosmological constant zero regardless of what happens to the brane tension by adjusting the deficit angle. We speculated that this self-tuning property would imply a massless scalar mode in the perturbed Einstein's equations; as there exist very stringent limits on scalar-tensor theories of gravity, a massless scalar mode would make this model incompatible with observation. We conducted a search for such modes, and found none which satisfied the boundary conditions. This finding led us to speculate that this model does not, in fact, have a self-tuning property.