Presumably the upconversion is lacking in quality, and the size of the screen is making this easy to perceive.

The solution is to get a Bluray player with excellent quality de-interlacing and scaling built in, and watch your DVD's with that. It won't make them look like HD, and it can't really improve a bad transfer, but well-encoded discs will be quite watchable.

The usual recommendation is to get an Oppo player, since it is the cheapest way to get first-rate upconversion. Anything of similar quality from other brands will cost much more.