Type ‘void’ is not assignable to type ‘ObservableInput’

you have to return the Observable

 return request
    .map((res: Response) => res.json())
    .catch((error: any) => {
        // todo: log?

        if (error.status == 500) {
            this.alertService.showError(error.statusText);
        } else if (error.status == 588) {
            this.alertService.showAlert(error.statusText);
        }

        return Observable.throw(error.statusText);
    });