Fui fazer o buil do projeto com a alteração da API_URL no webpack e recebi a seguinte mensagem de erro:
ERROR in build.js from UglifyJs
Unexpected token: punc (:) [./src/main.js:14,24][build.js:19093,73]
npm ERR! Linux 4.18.0-18-generic
npm ERR! argv "/usr/bin/node" "/usr/bin/npm" "run" "build"
npm ERR! node v8.10.0
npm ERR! npm  v3.5.2
npm ERR! code ELIFECYCLE
npm ERR! alurapic@1.0.0 build: `cross-env NODE_ENV=production webpack --progress --hide-modules`
npm ERR! Exit status 2
npm ERR! 
npm ERR! Failed at the alurapic@1.0.0 build script 'cross-env NODE_ENV=production webpack --progress --hide-modules'.
npm ERR! Make sure you have the latest version of node.js and npm installed.
npm ERR! If you do, this is most likely a problem with the alurapic package,
npm ERR! not with npm itself.
npm ERR! Tell the author that this fails on your system:
npm ERR!     cross-env NODE_ENV=production webpack --progress --hide-modules
npm ERR! You can get information on how to open an issue for this project with:
npm ERR!     npm bugs alurapic
npm ERR! Or if that isn't available, you can get their info via:
npm ERR!     npm owner ls alurapic
npm ERR! There is likely additional logging output above.
npm ERR! Please include the following file with any support request:
npm ERR!     /home/natan/Cursos Alura/Vue.js/alurapic/npm-debug.log
A linha 14 a que se refere o erro é justamente a linha do arquivo main.js em que é definido o  Vue.http.options.root:
import Vue from 'vue'
import App from './App.vue'
import VueResource from 'vue-resource';
import VueRouter from 'vue-router';
import { routes } from './routes';
import './directives/Transform';
import VeeValidate from 'vee-validate';
import msg from './pt_BR';
import 'bootstrap/dist/css/bootstrap.css';
import './assets/css/teste.css';
import 'bootstrap/dist/js/bootstrap.js';
Vue.use(VueResource);
Vue.http.options.root = process.env.API_URL ? process.env.API_URL : 'http://localhost:3000'
Vue.use(VueRouter);
const router = new VueRouter({ 
  routes, 
  mode: 'history'
});
Vue.use(VeeValidate, {
  locale: 'pt_BR',
  dictionary: {
    pt_BR: {
      messages: msg
    }
  }
});
new Vue({
  el: '#app',
  router,
  render: h => h(App)
})
Por fim, segue o código do webpack.config.js:
var path = require('path')
var webpack = require('webpack')
module.exports = {
  entry: './src/main.js',
  output: {
    path: path.resolve(__dirname, './dist'),
    publicPath: '/dist/',
    filename: 'build.js'
  },
  module: {
    rules: [
      {
        test: /\.vue$/,
        loader: 'vue-loader',
        options: {
          loaders: {
            // Since sass-loader (weirdly) has SCSS as its default parse mode, we map
            // the "scss" and "sass" values for the lang attribute to the right configs here.
            // other preprocessors should work out of the box, no loader config like this nessessary.
            'scss': 'vue-style-loader!css-loader!sass-loader',
            'sass': 'vue-style-loader!css-loader!sass-loader?indentedSyntax'
          }
          // other vue-loader options go here
        }
      },
      {
        test: /\.js$/,
        loader: 'babel-loader',
        exclude: /node_modules/
      },
      {
        test: /\.(png|jpg|gif|svg)$/,
        loader: 'file-loader',
        options: {
          name: '[name].[ext]?[hash]'
        }
      },
      { test: /\.css$/, loader: 'style-loader!css-loader' },
      { test: /\.(woff|woff2)(\?v=\d+\.\d+\.\d+)?$/, loader: 'url-loader?limit=10000&mimetype=application/font-woff' },
      { test: /\.ttf(\?v=\d+\.\d+\.\d+)?$/, loader: 'url-loader?limit=10000&mimetype=application/octet-stream' },
      { test: /\.eot(\?v=\d+\.\d+\.\d+)?$/, loader: 'file-loader' },
      { test: /\.svg(\?v=\d+\.\d+\.\d+)?$/, loader: 'url-loader?limit=10000&mimetype=image/svg+xml' }
    ]
  },
  resolve: {
    alias: {
      'vue$': 'vue/dist/vue.common.js'
    }
  },
  devServer: {
    historyApiFallback: true,
    noInfo: true
  },
  performance: {
    hints: false
  },
  devtool: '#eval-source-map',
  plugins: [
    new webpack.ProvidePlugin({
      $: 'jquery/dist/jquery.js',
      jQuery: 'jquery/dist/jquery.js'
    })
  ]
}
if (process.env.NODE_ENV === 'production') {
  module.exports.devtool = '#source-map'
  // http://vue-loader.vuejs.org/en/workflow/production.html
  module.exports.plugins = (module.exports.plugins || []).concat([
    new webpack.DefinePlugin({
      'process.env': {
        NODE_ENV: '"production"',
        API_URL: 'localhost:3000789'
      }
    }),
    new webpack.optimize.UglifyJsPlugin({
      sourceMap: true,
      compress: {
        warnings: false
      }
    }),
    new webpack.LoaderOptionsPlugin({
      minimize: true
    })
  ])
}
Existe algum erro no código?
 
             
            