We obtained very deep and high spatial resolution near-infrared images of the Orion Trapezium Cluster using the Multi-Conjugate Adaptive Optics Demonstrator (MAD) instrument at the VLT. The goal of these observations has been to search for objects at the very low-mass end of the IMF down to the planetary-mass regime. Three fields in the innermost dense part of the Trapezium Cluster, with a total area of 3.5 sq.arcmin have been surveyed at 1.65μm and 2.2μm. Several new candidate planetary mass objects with potential masses < 13MJup have been detected based on their photometry and on their location in the colour-magnitude diagram. The performance of the multi-conjugate adaptive optics correction is execellent over a large field-of-view of thicksim 1'. The final data has a spatial resolution of < 0.1arcsec over most of the area covered, enabling us to study the brown dwarf binary fraction, which is tightly linked to the brown dwarf formation process in dense stellar clusters. Only one brown dwarf binary was found, which is a newly detected system. Confirmation of the substellar nature of the faintest objects detected in our observations (potentially 3-10MJup), however, must await future confirmation by spectroscopic and/or photometric observations.