This program:

public class Bug {
    @SuppressWarnings("serial") final Throwable[] a = {new Throwable() {}};
    @SuppressWarnings("serial") Throwable[] b = {new Throwable() {}};
    public static void main(String[] args) throws Throwable {
@SuppressWarnings("serial") final Throwable[] c = {new Throwable() {}};
@SuppressWarnings("serial") Throwable[] d = {new Throwable() {}};
    }
}

should generate either zero or four warnings, but:

$ jver -v 7 javac -Xlint:all Bug.java
Using JDK /java/re/jdk/7/promoted/latest/binaries/solaris-sparcv9
Bug.java:2: warning: [serial] serializable class <anonymous Bug$1> has no definition of serialVersionUID
    @SuppressWarnings("serial") final Throwable[] a = {new Throwable() {}};
                                                                       ^
Bug.java:5: warning: [serial] serializable class <anonymous Bug$3> has no definition of serialVersionUID
@SuppressWarnings("serial") final Throwable[] c = {new Throwable() {}};
^
2 warnings

Clearly the use of "final" should make no difference.