When deserializing an object with a Map property that has an Enum type as a key, the Enum constants are not used. Rather, a new Enum instance (outside of the set of constants) is created. This makes the resulting dictionaries fields in the created BasicMap instance essentially useless... strict equality checks against those Enum keys always fail!

E.g.:

Our Java bean:
public class MyBean {
    public Map<MyEnum, String> myMap;

    ...
}

Our Flex bean:
public class MyBeanBase implements IExternalizable {
    private var _myMap:IMap;

    public get myMap():IMap {
        return _myMap;
    }

    public set myMap(value:IMap):void {
       _myMap = value;
    }

    ...

    public function readExternal(input:IDataInput):void {
        __initialized = input.readObject() as Boolean;
        __detachedState = input.readObject() as String;
        if (meta::isInitialized()) {
            ...
            _myMap = input.readObject() as IMap; // <- This does not deserialize the Enum keys properly (creates a new instances... does not use static constants)
            ...
        }
        else {
            ...
        }
    }
}

Some Flex client code:
var bean:MyBean = beanGeneratedFromRemoteObjectResult;
bean.myMap.containsKey(MyEnum.Red); // <- This is always false, since the enum key object is a different instance from the MyEnum.Red const instance