For your particular problem, you need to figure out what the target screen sizes are (probably mostly between 1920x1080 and 1366x768) along with the default zoom options and then increase those pattern sizes in your art to get out of the danger zone where moire is created.
Note that Acrobat/Distiller/whatever-they-call-it-now has a "default view" setting in "file > properties." While there is no gurantee of client software honoring it, you can set the view there and then save it. I like to set it to the "full-page, spread, with cover" setting so that it simulates a book.
The problem here is that you have a dynamic zoom and multiple client display devices with variant capabilities. You cannot avoid moire, you can only try and mitigate first impressions.
Moire patterns are a function of the content of the art and the sampling rate. On screen, the sampling rate is more or less the size of the grid of pixels (the desktop's pixel dimensions).
When patterns within the art are close to the grid size (and especially not strictly parallel to the x and y axes) you run the risk of moire. For any sample to be properly reconstructed you need the sample rate to be approximately 2x the frequency. ( http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem#Application_to_multivariable_signals_and_images )
Incidentally, this sampling 2x (really 1.5-2) number is the reason for "300dpi" standard in commercial printing. High-quality-but-common halftone screens are around 150 lines per inch. You need 300dpi to get above the 150lpi sampling frequency. But if you work for a screen door company, you need to be careful about your choice of art.