We propose a Multi-Instance-Learning (MIL) approach for weakly-supervised learning problems, where a training set is formed by bags (sets of feature vectors or instances) and only labels at bag-level are provided. Specifically, we consider the Multi-Instance Dynamic-Ordinal-Regression (MI-DOR) setting, where the instance labels are naturally represented as ordinal variables and bags are structured as temporal sequences. To this end, we propose Multi-Instance Dynamic Ordinal Random Fields (MI-DORF). In this framework, we treat instance-labels as temporally-dependent latent variables in an Undirected Graphical Model. Different MIL assumptions are modelled via newly introduced high-order potentials relating bag and instance-labels within the energy function of the model. We also extend our framework to address the Partially-Observed MI-DOR problems, where a subset of instance labels are available during training.We show on the tasks of weakly-supervised facial behavior analysis, Facial Action Unit (DISFA dataset) and Pain (UNBC dataset) Intensity estimation, that the proposed framework outperforms alternative learning approaches. Furthermore, we show that MIDORF can be employed to reduce the data annotation efforts in this context by large-scale.