You do not mention what the file format of the offending file(s), but I am guessing that they are likely some type of Postscript-based file, such as EPS or PDF. These files are more prone to causing RIP errors and output anomalies than simple raster-based formats like TIF or JPG.
If the file is postscript-based, try the following steps in the design application (Illustrator / Corel etc):
1) Reduce or eliminate vector effects where possible, including transparency and filter effects.
2) Where they cannot be eliminated, attempt to flatten them.
3) If that doesn't give the desired effect, rasterize those objects only
4) Worst-case is to bring the file into Photoshop and rasterize the entire thing there. This will remove spot colors and convert cut paths into pixels, so this is really the last option. Save as an Uncompressed TIF for best results.
After doing this step, you would need to being the pixel-based file back into a vector design app like Illustrator to add cut paths or other vector objects.
Paul