The software that creates the DVD files has nothing to do with whether or not the disc plays, Arnold. So I'm not sure what's going on or why you're getting so many fails. It could be that Premiere Elements writes to your disc too quickly.
Try using Share/Disc to burn your DVD files to a Folder on your computer rather than directly to disc. Then use ImgBurn to burn the VIDEO_TS folder to a disc. Make sure that you have the option to Verify selected.
Also, what brand of blank media are you using, the DVD-R's?
Some brands, like Memorex, TDK, recent Ritek and most "store brands" buy from the cheapest source that day, and then re-brand the discs with their logos. What can happen is that in a spindle of 50, you might get 4 - 5 different brands of blank media, though they all say "Memorex," or other.
The great free burning utility, ImgBurn, has a little feature, that can actually tell you who made the blank disc, and even the batch number. It is also a very good utility for burning a VIDEO_TS folder to a blank disc, and allows one to lower the burn speed, which is a good thing. That VIDEO_TS folder (and the VOB, IFO and BUP files) is what you get with Burn to Folder.