Sharepoint-hosted App - App Part Edit or Display mode detection

In Elements.xml file of App Part, append editMode token to Src attribute of Content tag
Note: _editMode_ token will be replaced automatically by 0 or 1 depending on the current mode.

<Content Type="html" Src="~appWebUrl/Pages/ClientWebPart1.aspx?{StandardTokens}&amp;editMode=_editMode_" />

Add following helper function in App Part Page to retrieve the parameters from query string.

function getQueryStringParameter(paramToRetrieve) {
     var params;
     var strParams;

     params = document.URL.split("?")[1].split("&");
     strParams = "";
     for (var i = 0; i < params.length; i = i + 1) {
          var singleParam = params[i].split("=");
          if (singleParam[0] == paramToRetrieve)
               return decodeURIComponent(singleParam[1]);
     }
}

Use following code to detect current mode.

var editMode = getQueryStringParameter("editMode");

if (editMode == "1") {
     alert("editMode");
} else {
     alert("displayMode");
}