The rules of this forum prohibit us from helping with material downloaded from the net that is copyrighted. That includes most commercially made movies.
Giving you the benefit of a doubt, we’ll assume what you have is not in that category.
First off, I would stop using Memorex +RW disks. If you want to use RW, stick with Verbatim. The Verbatim +R and -R blank media are also recommended quite a lot around here.
Next, you might want to try slowing down your burn speed. If you are burning at 8x now, try it at 4x.
The movies that you download are obviously not already in dvd format, so I assume they are .wmv, .avi, .mkv or .mp4…something of that nature. Check to see what type of audio they have. If you are starting with mp3 audio that is variable bitrate encoded, you can have problems converting to dvd video. (usually causes synch problems though, which you haven’t mentioned). One tool for examining your video is MediaInfo. http://mediainfo.sourceforge.net/en
When you convert using DVDFlick, do the movies play ok on the laptop from the hard drive? Before you burn to disk? If so, then your problems are in the media or burning process. If they already have problems at that point, then your problems lie in the conversion process. Figure out which one applies to your situation.
I’ve already given advice on the media/burning side, but for the conversion, you may have problems in your source, or in DVDFlick itself.
Another free program to try for conversions is FAVC. http://favcfavc.googlepages.com/ I would use the HC encoder that is included with it. And then use ImgBurn to burn to disk. It is a very good, free burning program and FAVC can be configured to burn automatically with it.