Full code after the jump.

The following example listens for the stateChange event to determine if the VideoDisplay control entered the VideoEvent.CONNECTION_ERROR state:

View MXML

<?xml version="1.0" encoding="utf-8"?>
<!-- http://blog.flexexamples.com/2007/07/23/detecting-a-connection-error-when-loading-an-flv-with-the-videodisplay-control/ -->
<mx:Application name="VideoDisplay_stateChange_connectionError_test"
        xmlns:mx="http://www.adobe.com/2006/mxml"
        layout="vertical"
        verticalAlign="middle"
        backgroundColor="white" >

    <mx:Script>
        <![CDATA[
            import mx.controls.Alert;
            import mx.events.VideoEvent;

            private function videoDisplay_stateChange(evt:VideoEvent):void {
                switch (evt.state) {
                    case VideoEvent.CONNECTION_ERROR:
                        evt.currentTarget.visible = false;
                        Alert.show(evt.currentTarget.source, "Unable to connect to video");
                        break;
                }
            }
        ]]>
    </mx:Script>

    <mx:VideoDisplay id="videoDisplay"
            source="http://www.helpexamples.com/flash/video/404.flv"
            stateChange="videoDisplay_stateChange(event);" />

</mx:Application>

View source is enabled in the following example.

Due to popular demand, here is the “same” example in a more ActionScript friendly format:

View MXML

<?xml version="1.0" encoding="utf-8"?>
<!-- http://blog.flexexamples.com/2007/07/23/detecting-a-connection-error-when-loading-an-flv-with-the-videodisplay-control/ -->
<mx:Application name="VideoDisplay_stateChange_connectionError_test"
        xmlns:mx="http://www.adobe.com/2006/mxml"
        layout="vertical"
        verticalAlign="middle"
        backgroundColor="white"
        initialize="init();">

    <mx:Script>
        <![CDATA[
            import mx.controls.VideoDisplay;
            import mx.controls.Alert;
            import mx.events.VideoEvent;

            private var videoDisplay:VideoDisplay;

            private function init():void {
                videoDisplay = new VideoDisplay();
                videoDisplay.addEventListener(VideoEvent.STATE_CHANGE,
                            videoDisplay_stateChange);
                videoDisplay.source = "http://www.helpexamples.com/flash/video/404.flv";
                addChild(videoDisplay);
            }

            private function videoDisplay_stateChange(evt:VideoEvent):void {
                switch (evt.state) {
                    case VideoEvent.CONNECTION_ERROR:
                        evt.currentTarget.visible = false;
                        Alert.show(evt.currentTarget.source, "Unable to connect to video");
                        break;
                }
            }
        ]]>
    </mx:Script>

</mx:Application>