Aliasing (and therefore moire, a type of aliasing) is a problem for almost all Canon DLSRs (as well as other manufacturers). The root cause is line skipping, whereby in order to get the necessary framerate only every third line of pixels is read from the chip.
If you have fine detail that is about the same size as a line of pixels then as the camera moves the detail will pop in and out of existence as it passes each active line of pixels.
The latest generation of sensors to be found in the 1DX and 5D mkIII apparently address this issue by reading the whole sensor and downsampling in order to produce the 1080p image.
The issue can be remedied to an extend by mounting an anti-aliasing filter (much stronger than the one in front of the sensor) on the lens. This blurs the image so that the detail will be spread over several lines, and not pop in and out as it crosses an active line of pixels.