This is a problem you'll see with Internet Explorer when your web map starts to get big, like when you have added a lot of layers to the map (e.g., shapefiles). Layers that are stored in the map rely on the browser to draw them. IE doesn't have the same capabilities as Firefox and Chrome, so you'll start to see these errors. If you can, I'd suggest switching browsers. If you can't switch browsers, you might try installing Chrome Frame, which effectively runs Google Chrome inside IE.
Thanks,
Mike