We discuss nuclear reactions which could play a role in Big Bang Nucleosynthesis (BBN). Most of these reactions involve lithium and beryllium isotopes and the rates for some of these have not previously been included in BBN calculations. Few of these reactions are well studied in the laboratory. We also discuss novel effects in these reactions, including thermal population of nuclear target states, resonant enhancement, and non-thermal neutron reaction products. We perform sensitivity studies which show that even given considerable nuclear physics uncertainties, most of these nuclear reactions have minimal leverage on the standard BBN abundance yields of 6Li and 7Li. Although a few have the potential to alter the yields significantly, we argue that this is unlikely.