The electron app itself can be inspected using the developer tools, available from the View menu:

However, this view does not expose the contents of the webviews for inspection. To open the developer tools for a webview, first access the console for the electron shell as above, and then run
document.getElementById("mattermostView0").openDevTools();
Use mattermostView0 to inspect the first opened tab, mattermostView1 to inspect the second opened tab, and so on. A new window will appear with the developer tools for that webview:
