When I rode the Sibelius from Helsinki, Finland to St. Petersburg, Russia, a few years ago, I remember Russian customs officials boarding the train at the last stop on the Finnish side and working their way through the train before getting off at the first stop on the Russian side. Seemed like an efficient, effective way to do passport control--no stopping.

The train crew may have even secured everyone's passports and visas as they boarded to make sure that everyone's passports got inspected--I can't remember for sure, but there had to be some way that they would have ensured no one was able to slip through the net.

Russia really doesn't like tourists--you have to get "invited" by a person or company inside Russia in order to get a tourist visa--and the cleared zone (at least 500 feet wide, with no vegetation--only sand) at the border still looked like it would be patrolled by the Red Army and crossers would be shot, so I'm sure they have strict border control measures on the train.