As the data on cosmic microwave background anisotropies improve and potential cosmological applications are realized, it will be increasingly important for theoretical calculations to be as accurate as possible. All modern calculations for inflationary-inspired fluctuations involve the numerical solution of coupled Boltzmann equations. There are many assumptions and choices to be made when carrying out such calculations. Here we go through each assumption in turn, pointing out the best selections to make in each case, and the level of inaccuracy expected through an incorrect choice. For example, neglecting the effects of neutrinos or polarization has a 10% effect. Varying input parameters such as the radiation temperature and helium fraction can have smaller, but noticeable effects. We also discuss a few issues which are more numerical, such as the k range and smoothing. Some short-cut methods for obtaining the anisotropy spectrum are also investigated, for example, free-streaming and tilt approximations; generally none of these are adequate at the few % level. At the level of 1% it is important to consider somewhat baroque effects, such as helium recombination and even minimal amounts of reionization. At smaller angular scales there are secondary and higher-order effects which will ultimately have to be considered. Extracting information from the subsidiary acoustic peaks and the damping region of the anisotropy spectrum will be an extremely challenging problem. However, given the real prospect of measuring just such information on the sky, it will be important to meet this challenge. In principle it will be possible to extract rather detailed information about reionization history, neutrino contribution, helium abundance, non-power-law initial conditions, etc.
