  We explore the effects of three-loop minimal supersymmetric standard model
renormalisation group equation terms and some leading two-loopthreshold
corrections on gauge and Yukawa unification: each being one loop higher order
than current public spectrum calculators. We also explore the effect of the
higher order terms (often 2-3 GeV) on the lightest CP even Higgs mass
prediction. We illustrate our results in the constrained minimal supersymmetric
standard model. Neglecting threshold corrections at the grand unified scale,
the discrepancy between the unification scale $\alpha_s$ and the other two
unified gauge couplings changes by 0.1$\%$ due to the higher order corrections
and the difference between unification scale bottom-tau Yukawa couplings
neglecting unification scale threshold corrections changes by up to 1$\%$. The
difference between unification scale bottom and top Yukawa couplings changes by
a few percent. Differences due to the higher order corrections also give an
estimate of the size of theoretical uncertainties in the minimal supersymmetric
standard model spectrum. We use these to provide estimates of theoretical
uncertainties in predictions of the dark matter relic density (which can be of
order one due to its strong dependence on sparticle masses) and the LHC
sparticle production cross-section (often around 30$\%$). The additional higher
order corrections have been incorporated into SOFTSUSY, and we provide details
on how to compile and use the program. We also provide a summary of the
approximations used in the higher order corrections.
