I'm sure you were intending this for an exercise in Web GIS, but I decided to bring your arcgis server to ArcGIS for Desktop for a try as a .lpk.
Fallbrook, San Marcos, and Vista all allowed me to create local copies for editting and able to sync back, while the Oceanside one doesn't even come in with the lpk file.
Within the web map, since all the food stores are symbolized the same, I can't tell which are which.
Also worth noting, I think your Fallbrook dataset came in with the lpk, but the dataset was empty, no points were showing on the map.