Rasterize it or make the gradient in Photoshop and place tat in AI and be done with the problem.
1. Any spot colors in your file? They bust down erratically when you leave it to the RIP to interpret them, especially when there are transparent objects interacting. You've probably seen the warning when you save your file so many times you don't read it anymore. You're not printing spot inks on the Epson, right? Try converting them all to process before printing.
2. A weird one. I don't know if it applies, but we run into an issue here where .psd's overlap each other and cause subtle (or not so subtle) postscript errors. Sometimes, it's garbled images, sometimes it's garbled vectors. Is the Epson a postscript printer? I usually see this one when there is a clipping path that's not really needed in a transparent file...
Try this. Export the file(s) as 150ppi, CMYK .tiff's > Open the .tiff file(s) in Photoshop > Save as .pdf; the file size may be bigger, but you may lose most of the artifacts. Another option is use Distiller to convert the Illustrator file(s) to .pdf; but use a lmedium res., live transparency compliant setting like PDF/X4.
Looking at your PDF it's difficult to tell exactly what's happening. I've had banding problems, however, in similar situations passing Illustrator files through Photoshop to be converted to high-resolution JPEGs for a very specific printer. Essentially, the file looks fine in Illustrator and fine in Photoshop until one significantly raises the white levels. The banding which then appears is very similar to the banding which appears upon printing. Can you see the errors in your file before they're printed? Or, only after printing?
Here's a couple thoughts... save Illustrator file as hi-res PDF. Use CS4 High-Quality Print presets. Open in Photoshop, rasterize at 300dpi in PS's opening dialog box. Flatten and save as TIFF, etc. for printing. May solve the problem.
Another setting to experiment with which may do nothing (and may cause the sky to fall) is to check your presets for Color Settings. Try setting Conversion Options > Intent > to Perceptual. This may make some users howl as Relative Colorimetric is the default setting for many users. However, it's been said to me that Perceptual is the correct setting to avoid banding in images with large gradients.
For more information on the differences between the two, check out: http://www.cambridgeincolour.com/tutorials/color-space-conversion.htm
Regarding the lines around placed images, I haven't dealt with that one. You may want to open the images in Photoshop and make sure there isn't some colored trim left over from the cropping process. Provided that isn't the case, try re-placing them before saving to PDF and moving to Photoshop.
Hope this helps.
Thank you to everyone who has sent a suggestion. I'm working my way through trying all of them.
In the meantime, I've found a 'Band Aid'. I printed to the PDF printer, and athough the white lines around items showed on my screen and on my office laser, they did not on the Wide Format printer that I sent it to. I had a problem with light colored boxes showing around text with drop shadows but I have, hopefully, corrected that and have sent the file to the Printer again to test.
Once I try everything that has been suggested, I'll come back and post a reply in the hopes that it will help someone else!