How can one carry out a "Russian style" seminar?
I use a version of this in the weekly research seminar that I run.
This format typically works best when 


the speaker knows ahead of time that he/she is likely to get questions during the talk and 
at least a few of the audience members feel comfortable asking such questions.  


If the speaker is a regular attendee of the seminar, then (1) works itself out naturally; otherwise, I recommend that the organizer mention this ahead of time to the speaker.  Generally, more experienced speakers are more comfortable with this model.  As I'm asking questions during the talk, I watch the speaker's responses.  If the speaker starts to get flustered or is unable to answer well a few questions in a row, then I often will stop asking questions.  Actually, I usually talk a little with the speaker ahead of time about what I'm hoping for from the talk, who the typical audience is, how long the talks usually go, etc.  I find that a few minutes beforehand can save you from the awkward experience of having a talk that is at too low or too high a level.

For (2), I am usually quite comfortable asking questions, and I generally find that at least one other faculty member in the audience is.  As Jeromy mentioned, typically this model works best when the questions are asked by well-informed audience members (since they can more easily discern which questions will and will not be helpful to the rest of the audience).  If you find that no one else in the audience is asking questions, I suggest that you talk with a few of the regular attendees and ask if they would be willing to start asking questions.  (This conversation probably will work better outside of the actual seminar.)