I had the same issue on my android application. The cause of the issue is FB login javascript opens a new page on a new window. Then it tries to close it after login success. Please follow flowing example from my working codes.
<FrameLayout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:tools="http://schemas.android.com/tools"
android:layout_width="match_parent"
android:layout_height="match_parent"
android:background="#0099cc"
tools:context=".MyActivity" 
android:id="@+id/webview_frame">
<WebView
android:id="@+id/webview"
android:layout_width="fill_parent"
android:layout_height="fill_parent"
/>
The Webview of id "webview" is the main view for my content. Below is my activity codes.
public class MyActivity extends Activity {
/* URL saved to be loaded after fb login */
private static final String target_url="http://www.example.com";
private static final String target_url_prefix="www.example.com";
private Context mContext;
private WebView mWebview;
private WebView mWebviewPop;
private FrameLayout mContainer;
private long mLastBackPressTime = 0;
private Toast mToast;
@Override
protected void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
setContentView(R.layout.activity_urimalo);
// final View controlsView =
// findViewById(R.id.fullscreen_content_controls);
CookieManager cookieManager = CookieManager.getInstance(); 
cookieManager.setAcceptCookie(true); 
mWebview = (WebView) findViewById(R.id.webview);
//mWebviewPop = (WebView) findViewById(R.id.webviewPop);
mContainer = (FrameLayout) findViewById(R.id.webview_frame);
WebSettings webSettings = mWebview.getSettings();
webSettings.setJavaScriptEnabled(true);
webSettings.setAppCacheEnabled(true);
webSettings.setJavaScriptCanOpenWindowsAutomatically(true);
webSettings.setSupportMultipleWindows(true);
mWebview.setWebViewClient(new UriWebViewClient());
mWebview.setWebChromeClient(new UriChromeClient());
mWebview.loadUrl(target_url);
mContext=this.getApplicationContext();
}
private class UriWebViewClient extends WebViewClient {
@Override
public boolean shouldOverrideUrlLoading(WebView view, String url) {
    String host = Uri.parse(url).getHost();
    //Log.d("shouldOverrideUrlLoading", url);
    if (host.equals(target_url_prefix)) 
    {
        // This is my web site, so do not override; let my WebView load
        // the page
        if(mWebviewPop!=null)
        {
            mWebviewPop.setVisibility(View.GONE);
            mContainer.removeView(mWebviewPop);
            mWebviewPop=null;
        }
        return false;
    }
    if(host.equals("m.facebook.com"))
    {
        return false;
    }
    // Otherwise, the link is not for a page on my site, so launch
    // another Activity that handles URLs
    Intent intent = new Intent(Intent.ACTION_VIEW, Uri.parse(url));
    startActivity(intent);
    return true;
}
@Override
public void onReceivedSslError(WebView view, SslErrorHandler handler,
        SslError error) {
    Log.d("onReceivedSslError", "onReceivedSslError");
    //super.onReceivedSslError(view, handler, error);
}
}
class UriChromeClient extends WebChromeClient {
@Override
public boolean onCreateWindow(WebView view, boolean isDialog,
        boolean isUserGesture, Message resultMsg) {
    mWebviewPop = new WebView(mContext);
    mWebviewPop.setVerticalScrollBarEnabled(false);
    mWebviewPop.setHorizontalScrollBarEnabled(false);
    mWebviewPop.setWebViewClient(new UriWebViewClient());
    mWebviewPop.getSettings().setJavaScriptEnabled(true);
    mWebviewPop.getSettings().setSavePassword(false);
    mWebviewPop.setLayoutParams(new FrameLayout.LayoutParams(ViewGroup.LayoutParams.MATCH_PARENT,
            ViewGroup.LayoutParams.MATCH_PARENT));
    mContainer.addView(mWebviewPop);
    WebView.WebViewTransport transport = (WebView.WebViewTransport) resultMsg.obj;
    transport.setWebView(mWebviewPop);
    resultMsg.sendToTarget();
    return true;
}
@Override
public void onCloseWindow(WebView window) {
    Log.d("onCloseWindow", "called");
}
}
}
The key for this issue is onCreateWindow. A new window is created and inserted to the frame layout and removed upon success. I added the removal at shouldOverrideUrlLoading.