Are there no statute of limitations on a traffic fine that is 25 freakin' years old even if you had not paid it? The insanity of it all.

I'm not a lawyer but I think that the statute of limitations applies to the time between the offense and its adjudication.

If I tell a cop I smoked a joint thirty years ago he can't arrest me for it.

Once the perp has been found guilty, as I assume was the case here, s/he has to pay the penalty unless pardoned, there's no time limit that I'm aware of; in fact, dodging the penalty could and usually does increase its severity until an arrest warrant is issued, but the exact procedure could vary with the jurisdiction.