I think this topic will sit better in the Swing forum, so I shall move it . . .
Those warnings are actually found on the API for every Swing class I have ever used, so I think it is there for them all. What it means is that serialisation should only be used for sending them across a network or short-term storage. But how often do you want to store a Frame or send it across a network? You often store objects representing the data to go with a Swing GUI, but that is something different. There is the Beans framework which can also be used to store objects, which is what you are supposed to use for Swing, but I know little about it myself. So you don't need to worry that your objects will somehow become obsolete; in fact Sun have taken great pains to maintain backward compatibility for older versions of
Java.
The warning about thread-safety is more serious; it means that everything which affects any of your GUI components must be coded on the same thread. If you just code it in the classes as usual and don't do anything like creating a new Thread, or a new Runnable, then it will all be on the same thread.
So as to ensure you are on the event despatch thread (EDT) there is a special invocation, whereby your entire GUI is inside a single Runnable. There are two examples on the API; where you found the warning there is a link marked "Swing Threading Policy" or similar, where you will find two examples of starting GUIs with invokeLater() and also the correct spelling of EDT.
Hope that helps for a start, and that you get more answers on the other forum.