Node Module Version Mismatch: Expected 50

This is a known issue which is caused by the serialport module using native code that is built for a different version of Node. You can read a bit more about addons here, if you're interested; they're just modules written in C/C++ that can interface with Node so the module can interface with the hardware more easily.

The solution proposed by that issue is this:

npm rebuild --runtime=electron --target=1.2.5 --disturl=https://atom.io/download/atom-shell --build-from-source

If you've not already installed electron-rebuild, that might be helpful to ensure that the rebuilding process works correctly:

npm install --save-dev electron-rebuild

even though when I run node -v it prints v6.6.0, running process.versions.node in the web console gives me v6.5.0. What's going on here?

Electron uses its own version of Node that isn't connected to your system Node installation (see the homepage to view the Node version that the latest Electron uses, or use process.versions.node, like you did in the question).

You could try an older version (perhaps 1.1.0, which uses Chrome 50?) in case that is the cause of the issue.