There are many ways of interpreting the world and they are highly interdependent. We exploit such complex dependencies and introduce a powerful multi-task hypergraph, in which every node is a task and different paths through the hypergraph reaching a given task become unsupervised teachers, by forming ensembles that learn to generate reliable pseudolabels for that task. Each hyperedge is part of an ensemble teacher for a given task and it is also a student of the self-supervised hypergraph system. We apply our model to one of the most important problems of our times, that of Earth Observation, which is highly multi-task and it often suffers from missing ground-truth data. By performing extensive experiments on the NASA NEO Dataset, spanning a period of 22 years, we demonstrate the value of our multi-task semi-supervised approach, by consistent improvements over strong baselines and recent work. We also show that the hypergraph can adapt unsupervised to gradual data distribution shifts and reliably recover, through its multi-task self-supervision process, the missing data for several observational layers for up to seven years.