My Russian visa experience: I was going to a meeting with some scientific collaborators at an institute near St. Petersberg. They faxed me a letter of invitation, and I had all of the application documents in order. I took everything in person to the consulate in San Francisco and found that they were closed for some Russian holiday that was not listed on the calendar on their web site. I tried again the next day, waited in line for half an hour, and the person behind the window looked at the invitation letter and nearly screamed "WHAT IS THIS ABOUT?" at me. I explained what kind of research we do, and he replied with "the consul will consider this application." I came back the next week to pick up my passport, and it had a visa in it, so I guess there was no problem in the end.
St. Petersberg is a truly beautiful city, BTW--it's worth the paperwork hassle to go there, especially in the summer during the White Nights.