KFdancer, thank you so very much for your reassurance. I'm sure I'm not the only person to cross the Home Office who has made this sort of mistake.
I will grant that, at the time, it was incredibly traumatic. When the officer, who had booked a massage appointment and proceeded to goad me into offering lewd ending possibilities (in addition to denying being a police officer when asked, of course) revealed himself, two of his associates entered with guns drawn. I was alone, unarmed, and clad in a bikini. The female officer drew her gun, and pointed it at my temple, as the additional gentleman searched the room for "drugs, weapons, and scary boyfriends". Finding nothing of the sort, the police led me to their vehicle, booked me into the detention facility at the city jail, and held me for the night until my roommate came by with bail. During my nearly 20 hours in the holding area, I was surrounded by some folks who were rather hardened sorts and others who appeared to be under the influence of exotic substances. There was one TV and one bible for entertainment, so I spent the majority of my time attempting to collect stories from the less-intimidating ladies.
My court date and the terms of my unsupervised probation (fine, class, AIDS test) went by without incident, and I was never affected by that summary probation as I never did another thing wrong (save minor traffic violations). I was able to find work without incident. However, the night of my arrest continued to haunt me, and to this day I struggle with the thought that I must be a horrible person for the police to think it prudent to hold a gun to my head when I was being completely cooperative (albeit tearful and shaken).
For the most part, I'd managed to confine this horrifying memory to the back of my mind until Ross proposed. That's when I began panicking and beating myself up all over again.
On my FBI record, my single offence is listed as "001 count of Disorderly Conduct Prostitution; California 247b(pc), followed by "Penalty Probation 3 years/fine/ restn/work program". It has, as mentioned, not been updated with the dismissal, but I think the UK Home Office will find it satisfactory evidence that I am basically a good person who made one stupid mistake (plus, we have included quite a bit of concrete evidence of the subsequent dismissal).
I never obtained a copy of the initial police report during or following my case, so I my lawyers and I were not able to submit that to the HO. However, my lawyers and I have submitted the court records, order for dismissal, pubic record screencap, and FBI record. My lawyers feel this will be enough.
I am sorry for being so horribly whiny and self-indulgent in this thread, and temporarily assuming the role of "Little Miss Overshare". If any of you have horror stories of your own to share, please feel free. I am always available for hugs and reassurance. It is my firm belief that, at heart, the VAST majority of people are kind and good.

::joins in the group hug::
Much love,
Rachel