I am presently using 1 click DVD along with AnyDVD 5.6.3.1 , and get the full movies until the last 10 minutes or so, then it skips and I see digital pixel squares on the screen. Any ideas?

Try decreasing your burn speed to 4x .
Also I might look at the quality of media that you are presently using .

You could stop by the 1Click forum for some more pointers

As stated previously, I would check the type of media you are using.

Also, shut down any background process that might have started up while burning..... Virus Scan, Computer Power management, etc etc.

What Shannon and Nefarious said, plus -- if you are copying more than movie only, why not try some movie only. That will reduce the amount of compression needed. High compression is a contributor to pixelizing. The reason it's coming late in your movies is that burns are from the inside out on the disk. Out near the edge, errors, imperfections and anything else that can cause problems is magnified. Also, some players tend to pixelize more than others.

any recomendations on the media type to get best results???

Usually you can count on anything made in Japan, but there are some exceptions, like Verbatim. Sony labeled dvds are also generally good. The gold standard is anything made by Taiyo Yuden (as many Sony tend to be). You can buy Taiyo Yuden from several on-line vendors, and www.supermediastore.com is a good one.