For consideration.

These warnings are already covered by renderers based on react-reconciler. Maybe we don't gain that much by mirroring them in the shallow renderer? Maybe it's not worth the added complexity? Particularly with more complicated warnings like the ones being added for #12419 and #12404.
constructor(props) {
        super(props);
        this.state = {
          bar: 'bar',
        };
      }
      render() {
        return <div>{`${this.props.foo}:${this.state.bar}`}</div>;
      }
    }
    const shallowRenderer = createRenderer();
    const el = <SimpleComponent foo="foo" />;
    let result = shallowRenderer.render(el);
    expect(result).toEqual(<div>foo:bar</div>);
    const cloned = React.cloneElement(el, {foo: 'baz'});
    result = shallowRenderer.render(cloned);
    expect(result).toEqual(<div>baz:bar</div>);
  });
  it('this.state should be updated on setState callback inside componentWillMount', () => {
    let stateSuccessfullyUpdated = false;
    class Component extends React.Component {