Brian - please let us know if this resolves your need. Based on your description, I am guessing that the 'Max Number of Rasters per Mosaic' property (as mentioned by Peter) can enable you to display the missing rasters, but I thought it would be worth a bit more explanation re: "Why?".
re: 'Max Number of Rasters per Mosaic', we set a default of 20 to prevent poor performance if you attempt to view too many files. Yes, you can increase that value, and also adjust MinPS and MaxPS, but if you zoom out and expect to see hundreds of small images (requiring ArcGIS to open and display a large number of files) the result can be slow, especially if the source rasters don't have Pyramids.
This leads to other key issues to consider, including the use of Pyramids and Overviews (the latter mentioned by Ben). If you aren't familiar w/ them, both are reduced resolution views saved on disk to speed display. Pyramids are associated with each source raster, and Overviews are conceptually the same, but associated with the mosaic of multiple rasters. In my 2nd paragraph I referred to opening hundreds of files - If pyramids do not exist, ArcGIS has to resample each raster on the fly to generate the proper resolution, and that will take time. But even if pyramids do exist, we don't recommend attempting to display hundreds simply because opening a large number of files will still take time (thus the default of 20 individual rasters).
As Ben noted, when you zoom out, the system will automatically switch to displaying the appropriate Overviews if they exist. These are prebuilt reduced resolution views of the mosaic - so rather than displaying hundreds of individual rasters, you should have a very fast display of one or a small number of Overviews.
I hope this explains why you see green wire frames rather than images. You called it a "typical problem" but this is how the system was designed, to avoid slow performance. (You might ask "well, why doesn't ArcGIS just do this automatically?" but think about the case of thousands or millions of images - users would be very angry if we automatically started a process to generate Pyramids and they had to wait for hours just to see if the images were in the right place -- thus the green wireframes)
Two last notes: when you create Pyramids or Overviews, I recommend that you use Bilinear resampling rather than Nearest Neighbor, so the results look smooth. But no matter which resampling method is used, when you are working with raster versions of maps, at small scales you may find the view is not very useful. In that situation, I often recommend that you add a completely different dataset at an appropriate resolution (e.g. Landsat imagery, or a hillshaded terrain, or a 1:1,000,000 map etc.). It does not show your data, but it provides geographic context.
If you would like to read more, we have published the Image Management Guidebook that provides discussion of all of these parameters.
I hope this is helpful
Cody B.
