It is not a good idea to combine ANY teflon pan with an automatic dishwasher, regardless of what the manufacturer says.
But fortunately for you, I have handy the Cook's Illustrated from October 2010, which did a nonstick skillet (aka frying pan aka saute pan) review. According to them, even the best nonstick coatings won't survive more than a year or two of heavy use. This makes proper care all the more important. Brand also isn't a good indicator of coating quality, because many pan manufacturers buy coatings from the same suppliers. To quote the article:
Most cookware manufacturers don't make their own nonstick coating; they buy it from suppliers offering a menu of options, from basic to premium, and spray it on their pans. It's similar to painting a room; the quality of nonstick coating is determined not only by what's in it but also by how carefully it's applied and cured, and how many coats the manufacturer decides to put on.
They found the Tefal (T-Fal in the States) Professional Total Nonstick Fry Pan ($35) had a nonstick coating that outperformed the other pans by a significant margin, probably due to its 5-layer nonstick coating (most pans use 2-3 layers). The only fly in the ointment was its handle, which had rivets that loosened after abuse. But, for $35 that isn't bad, doubly because it outperformed the $150+ All-Clad nonstick pans they used normally.
If you're looking for something cheaper than that, I'd suggest you look at construction and not brand. Pick a heavy pan (for its size), with either solid, thick-gauge aluminum OR a multi-ply construction. This combination ensures the pan will heat evenly and rapidly (crucial for eggs), and is resistant to warping (important if you use an electric range). If you're cooking eggs, avoid hard-anodized aluminum interiors, as they don't help prevent adhesion of eggs, and just cost more. The nonstick layer should look thick and smooth, not slightly textured.
My most-used frying pan (the default egg pan) is a small T-Fal that cost all of $7. The important thing is that it has the right construction and I treat it correctly; I'm careful not to scratch the surface with utensils, I never use a scouring pad on it, and it can't go near the dishwasher. This makes more of a difference than picking a fancy brand.
There is no risk to the Teflon itself, or from it; PTFE breaks down at about 500 F, which rice cookers will not achieve, especially on warming setting. Other than that, PTFE is one of the most inert substances known to man, as the atoms are already bound in energetically very favorable bonds: little is as able to displace them without significant input energy (thus the high breakdown temperature).
On the other hand, you should not hold rice for a long time without either refrigerating it, or having it above 140 F (60 C) as there is some risk of Bacillus cereus growing and causing food borne illness.
Best Answer
I had a quick look around pubmed, an aggregator of biological and medical literature, and found very little in the way of actual scientific evidence for teflon toxicity under 500C. In fact, teflon is still widely in use in surgery and can be left inside the body for tens of years.
This does not mean that improper operation (such as overheating to the point of thermolysis) cannot result in compounds you would rather not have in your food. It will also ruin the pan. Don't do it.