I dropped a piece of plastic into the hole where the lint screen goes. I don't want to start a fire, but am not sure how to get it out. Any ideas?

Disassembly (at least partial disassembly) is probably the only way you'll get to it. If you can get hold of a long "grabber" tool, you might be able to get it -- if the tool is long enough and if you can see the plastic.

It's very unlikely you'll have a fire in any case. Nevertheless, it would be a good idea to get it out.