A script like

class C {
  int x
}
def c = new C()
c.x = 5
sh "echo ${c.x}"

will fail since the local variable c is of a nonserializable type. You need to explicitly say

class C implements Serializable {
// ...

Since groovy-cps demands that local variables may be serialized, any locally defined classes must also be serializable (unless they are only ever being passed to binary methods: legal but unlikely).

Perhaps the transformer could implicitly add implements Serializable to any class declarations it finds. Generally this is harmless: if the class in fact contains some nonserializable fields, trying to serialize an instance will still fail in a predictable way.