I'm not quite sure i understand the question.
Are you saying you are downloading an avi and then
transcoding these to full MPEG2 DVD-rs to play in an old DVD player?
This process is
not recommended. MPEG4 is actually a superior method of encoding than MPEG2 and there's a huge loss of quality downgrading to MPEG2 DVD-r.
What is a method that will save you
vast amounts of time is to buy a piece of hardware that can playback MPEG4 (so called divx standalones), they are very, very cheap these days, and this will save you vast amounts of time, money and most of all quality.
You can burn avi files as data onto a DVD-r (just drop 6 avis @ 700mb on a Data project) and play in a divx/xvid standalone.
Personally I think your mad to settle for old technology if you are indeed using a old crappy dvd player.
My personal setup is an Xbox (first one, not a 360), which i've modified. You can get a second hand one for £50 and modification will cost about £10-20 which you can do yourself. i have this networked so just play avis from network shares, but can play off of dvds too. Its a far better options.
Other users have opted for branded divx players, which play avi files from data dvdrs but are very underpowered and have problems with things like custom matrices and advanced profile xvid. They'll play most stuff. You can pick one up for ~£30 pretty much anywhere these days. Still no where near as good as an Xbox 1 modified with XBMC.
The problem is that transcoding is a poor, extremely lossy solution and there's provbably been a glitch in the transcoding process. That's to be expected, its only a quick 1 pass of the original file.
If you want to encode with any kind of quality, and i warn now that its just a collosal waste of time that's way more valuable than to faff around with something that's going to give you something that looks worse than the original, you need to use CCE+a dvd mastering software.
Just not worth it, get a piece of hardware that can play xvids, preferably modify an xbox (don't let the 'games console' status discourage you, i've not played a game on it for about 2 years, i don't even know where my pad is but apart from my pc its my most used and most prized electronic equipment
)