ESP8266 "ERROR: Not connected to the internet" on save()

It's because the line require("ESP8266WiFi_0v25").connect is being executed when the code is uploaded to the board, rather than after save(). To fix it, just put that code into an function called onInit:

var soc;
var wifi;
function onInit() {
  Serial3.setup(115200, { rx: D9, tx : D8 });
  wifi = require("ESP8266WiFi_0v25").connect(Seri­al3, function(err) {
    if (err) {digitalWrite(LED4,1);throw err;}
    //wifi.at.debug();
      console.log("Connecting to WiFi");
        wifi.connect("Espruino",'freeWifi', function(err) {
          if (err) throw err;
          console.log("Connected");
          require("net").createServer(function(c){­
            console.log("incomming connection");
            c.on('data', onDataCallback);
            c.on('close', function(){
              console.log("bye");
            });
            soc = c;
          }).listen(8080);
          wifi.getIP(function(err,ip){
            if(err === null){
              console.log(ip);
              serverIP = ip;
              digitalWrite(LED2, 1);
            }
          });
    });
  });
}

function onDataCallback(data){
  digitalWrite(LED1, !digitalRead(LED1));
  console.log("Server received: " + data);
  if(data !== undefined){
    if(data.length >= 6 && data.substr(0, 3).toLowerCase() == "led"){
      switch(data.charAt(3)){
        case '1':digitalWrite(LED1, data.charAt(5));break;
        case '2':digitalWrite(LED2, data.charAt(5));break;
        case '3':digitalWrite(LED3, data.charAt(5));break;
        case '4':digitalWrite(LED4, data.charAt(5));break;
      }
    }
    soc.write("Response: " + data);
    if(data.substr(0,4) == "exit")
      soc.end();
  }
}