The thing about a "thimble full of plutonium" is one of the most overused and horribly incorrect urban myths about nuclear material in existance. Plutonium is nasty stuff and you don't want to be ingesting it, but it is not as horribly toxic in either a chemical or radiological sense as that statement implies. Cyanides, Hydrogen Sulfide, Arsenic, Mercury, etc. are more toxic chemically. Radium, polonium, radon, and certain isotopes of other elements have MUCH shorter half-lives and decay in a MUCH more energetic manner than plutonium. Your teacher probably said the "thimble fallacy" because he/she heard it someplace and has failed to do his/her research on the topic.
With Chernobyl, the problem there exited because a very unstable governmental situation over there at the time and because of the inexplicably poor design of the nuclear power plant. Over in Russia, they were more concerned with taking the spent fuel and recovering whatever fissile material they could from it. The safety of the workers, or the people in the area, were the least of their concerns. The accident happened because all safety procedures were NOT followed and all backup safety systems were turned off so they could see how far they could push the reactor. Here in the United States, and throughout much of Europe, the designs of nuclear power plants are MUCH stiffer in regards to the safety systems. Three Mile Island is a great example of this. There was a failure in one of the systems in the plant, but numerous backups and the physical design of the plant itself prevented ANY escape of radioacitve material from the site. (I wrote a massive paper about the TMI incident while in college. There were no confirmed reports of an increase in radiation levels outside of the containment buildings. Only heresay reports by random people with no actual readings given).
Where you do pose a valid point is in regards to the "waste". Right now, they simply have not come up with a valid way to handle the very high level wastes that come out of nuclear power plants. At the moment, they have to sit in a holding pool for about ten years in order for the shorter half-life materials to decay so that they can actually move in there and reprocess the material. If we can figure out a way to safely reprocess this HIGHLY radioactive waste we could reduce this problem. This is where building reprocessing facilities in conjunction with the plants at the same site could save some trouble. The plant uses the fuel, it comes out and is immediately reprocessed by the reprocessing plant, then it is put right back into the reactor. However all steps of this process will also require some quanitity of the "fossil fuels" in regards to building the plants, extracting the ores, etc. etc.
For the fusion reactors, the reason right now why they aren't being used is that they have yet to come up with a working reactor that produces more energy then it consumes. If it takes you 10 kilowatts to produce 8 kilowatts of energy, you're not going to be doing anybody any good.