speeding ticket received in Tacoma by police who did not use radar, possible defenses

The problem is what do you mean by documented proof? If a cop tails you for a 100 yards and uses that tail as an estimate for your speed most courts will accept that. Your friend may have a defense if he didn't tail her long enough to be able to estimate her speed.

It is difficult to ascertain how the officer measured your girlfriend's speed, but if the speed could have been obtained properly in any way by an moving in the opposite direction of a target vehicle, then the device used would probably be moving radar potentially backed by some sort of visual estimation (e.g., a guess).

Your girlfriend should fight a speeding infraction because speeding tickets affect a person's insurance premiums and driving record.

The officer does have to provide some written proof, but it's not proof beyond a reasonable doubt; rather, the burden of proof, while on the State or City, is a preponderance (a standard akin to 'more likely than not'). The officer does not even need to show up at the hearing absent a proper demand. Of course, your girlfriend can make a formal demand for some documentation several weeks before the hearing and provided she does everything properly, she will be allowed to obtain certain information.

The officer's testimony at trial would be sufficient to prove that your girlfriend was driving faster than the posted speed limit. A witness can generally testify as to the speed of an automobile. Officer's are often trained to determine speed by their own reckoning as well. That does not mean that a jury or a judge will believe the officer's testimony or that the officer would even remember that your girlfriend was speeding. That's what trials are for.