Simple tools for studying the effects of inter-fraction and inter-field motions on intensity modulated proton therapy (IMPT) plans have been developed, and have been applied to both 3D and distal edge tracking (DET) IMPT plans. For the inter-fraction motion, we have investigated the effects of misaligned density heterogeneities, whereas for the inter-field motion analysis, the effects of field misalignment on the plans have been assessed. Inter-fraction motion problems have been analysed using density differentiated error (DDE) distributions, which specifically show the additional problems resulting from misaligned density heterogeneities for proton plans. Likewise, for inter-field motion, we present methods for calculating motion differentiated error (MDE) distributions. DDE and MDE analysis of all plans demonstrate that the 3D approach is generally more robust to both inter-fraction and inter-field motions than the DET approach, but that strong in-field dose gradients can also adversely affect a plan's robustness. An important additional conclusion is that, for certain IMPT plans, even inter-fraction errors cannot necessarily be compensated for by the use of a simple PTV margins, implying that more sophisticated tools need to be developed for uncertainty management and assessment for IMPT treatments at the treatment planning level.