I haven't had a problem, the minimum is 300 DPI for everything done in Photoshop. If you need an exact or close to exact color match the printers ask you to use CMYK colors (it's an option in Photoshop). I use regular RGB colors and haven't noticed a big color difference. I guess if the colors are way off it won't work with their print process. Now that a lot of companies (especially online) use a digital process for printing I think there is more flexibility in the colors. I'm sure they also have their own process to turn colors CMYK if they are not correct.
I think it also depends on the printing company you use and how familiar they are with different files and file formats. From what I've been told vector based designs are better, but I really don't know how to use Illustrator so I just use Photoshop.
I had a printer tell me they could use .jpeg files and I sent them a .jpg and they told me it wouldn't work. I renamed the file to .jpeg (it worked fine on my computer) and they told me it still didn't work. I told them I could create pretty much any format they could use and for some reason we couldn't get my files to work. I then went to another printer and sent them the same .jpg and it worked fine.
Some formats that seemed preferable for several printers are .tiff, .jpg, .psd, .eps, .pdf. Some printers you mention them a format and they don't know what you're talking about.
I'm still experimenting with different printers because I've recently (in the last few weeks) designed several business cards (for myself) and I'm comparing quality, card stock, etc... Quality and file formats really range greatly from printing companies.