I have wondered the same thing. I'm not a compiler/interpreter writer, but I think the answer will be that it is impossible to get it perfect. However, you can get it correct in most cases.
First, I'm going to change the name "dynamic" language to "interpreted" language which is what I think of with Ruby, Javascript, etc. Interpreted languages tend to take advantage of run-time capabilities.
For instance, most scripting languages allow the following
-- pseudo-code but you get the idea
eval("echo(a)");
I just "ran" a string! You would have to refactor that string also. And will a be a variable or does this language allow you to print the character a without quotes if there is no variable a?
I want to believe this kind of coding is probably the exception and that you will get good refactoring almost all of the time. Unfortunately it seems that when I look through libraries for scripting languages, they get into such exceptions normally and maybe even base their architecture on them.
Or to up the ante a bit:
def functionThatAssumesInputWillCreateX(input)
eval(input)
echo(x)
def functionWithUnknownParms( ... )
eval(argv[1]);
At least when you refactor Java, and change a variable from int to string, you get errors in all the places that were expecting the int still:
String wasInt;
out = 3 + wasInt;
With interpreted languages you will probably not see this until run-time.