I deal with vector rips a bit at work, so maybe I can help a little. We're printing conductive ink with 10um features, so we've run into lots of ripping issues in the past.
I'm assuming this is inkjet printing? If it's screen printing, see the bottom of my response.
I might be telling you stuff you already know, but here's my insight. Ultimately any vector art will have to be ripped into a pixel format. This can be done either at the printer driver, from the vector program, or in a specialized pre-press software, such as EskoArtwork. The fact that you can see individual pixels tells me that the rip isn't at high enough resolution. They might be applying a standard DPI (or DPCM in your case) setting that works for advertising, but not for your application. You might ask them if they can do a finer pixel size, but they might be limited by the print head. Some wide format industrial inkjets have pretty large droplet sizes to increase throughput.
Regarding the missing pixels, this could be a dirty print head, or it could be sampling/aliasing if the resolution of the rip is too low. In my application, I'm printing 10um lines at 500um spaces for conductive grids for solar cells. If the image is ripped or printed at <1200DPI, entire lines disappear (similar to recording a 20KHz sine wave at 10KHz sampling rate, every other peak disappears). Between 1200 and 2400DPI, the lines move due to aliasing and we get bad moire patterns.
If it's screen printing, then the pixels are a function of the mesh size being used. The mesh's thread count defines "pixel" sizes. You can make a screen with a 2400DPI photomask, but the mesh will still "downsample" the print to the thread count. There are some fine polyester meshes available for printed electronics with resolutions of about 50um, but these small apertures are prone to clogging and can themselves cause missing areas of the print (particularly in lighter tinted areas). If it's a screen print, let me know and I can suggest a source for finer mesh screens, but in my experience, screen printers often make their own screens and are hesitant to try new meshes or third party screens, particularly for small runs.
-Chris