Can an MRI scan miss what a CT scan would show?

A CT scan is a computer-assembled set of X-rays taken from different vantage points. The computer can create 3D models of whatever it images, but the nature of X-ray imaging is that it is more effective for denser tissues (bone), than soft-tissues (organs or blood). There are new CT techniques that can help image organs (the heart is of particular interest), but MRI is generally capable of imaging soft tissues with greater detail. MRI is more frequently used for neurological imaging, and can be used to do chemical analysis of tissues (spectroscopy) inside your body non-invasively.

Because they use very different means to image, both CT and MRI can 'miss' things that would better show up on the other modality.