DC Union Station

Is there a rule at Union Station that says persons without a ticket cannot go onto the platforms?
If this is the case, where is the best spot to see trains at Union without a ticket?

A good location is actually outside the station. Go out the front entrance and then go east, then north up 2nd Street NE. After a couple of blocks you'll come to the building holding Amtrak's Washington Division offices at 900 2nd Street NE on the left. There's a parking lot on the north side of the building that provides an excellent view of trains coming and going, and there shouldn't be anyone hassling you about taking pictures inside the station or asking if you're a ticketed passenger.

Couple of other locations:
The upper deck of the parking garage.
The platform at the New York Avenue metrorail station.

There is also a small cafe at the facility mentioned on 2nd Ave so you could order a sandwich and watch trains all day.

ditto, the Railway News Stand is great...it's eye-level with the Union Station yard and there's always something going on. The bonus is that you can have a snack and sit down while you do it.