It would be great to output console errors as well. At the moment, when I don't run tests via command line and use only extension, I don't know when my components output console errors during tests. I mean these ones:

The output is shown in the Jest output channel. You can show to it using the Jest: Show Test Output Channel command (in the palette) or clicking on Jest in the status bar.

/cc @orta - Any preference on how to document features? I noticed today I didn't add any when adding the jest.runAllTestsFirst setting
I tried today and it doesn't show errors returned from react components.
That's unexpected! Would you be wiling to debug the extension? If not, could you reproduce the issue in a simple repo we can troubleshoot? It's possible that the error is printed when Jest runs all tests but not when you run it in watch mode, the output might be cleared.
Yes, will to this tomorrow.
Awesome. If you're going debug the extension, I'd start with breakpoints in src/JestExt.ts in the on('executableOutput', callback and in testsHaveStartedRunning().
The CHANGELOG is mainly how I document things - it shows up in the vscode page, but the extensions auto-update, so most don't see it
Did you figure this one out @yantakus? If not, how can we reproduce the issue?