Answer: Three
While it is true that the Order Of The Sith adheres strictly to the "Two Sith - no more, no less" rule, three Sith Lords appear in this movie.
Count Dooku is a Sith Apprentice known as Darth Tyranus. He is killed in battle by Anakin Skywalker early in the movie.
Anakin Skywalker later turns to the Dark Side, and pledges himself as a Sith Lord, replacing Count Dooku as the Sith Apprentice, and becoming Darth Vader.
Of course, Darth Sidous continues on throughout the entire movie as the Sith Master.
I PROMISE YOU THIS QUESTION IS CORRECT! THIS QUESTION HAS BEEN CHECKED AND RE-CHECKED EVERY WAY TO SUNDAY. IF YOU THINK YOU HAVE FOUND SOME BRILLIANT NEW TECHNICALITY FOR A CORRECTION NOTE, PLEASE DO NOT WASTE YOUR TIME, MINE, OR THE EDITORS'.
However, if you still feel a need to enlighten us, please make sure you read the following paragraphs, as they deal with some of the more common correction notes sent by players:
(1) There has been some confusion about what constitutes a Sith Lord. Sith Lords need not be Masters to carry the title Lord. To be a Sith Lord one need only be an Apprentice. There are always two Dark Lords of the Sith: The Master and Apprentice. That is why, in "Episode II" Sidious refers to Count Dooku as "Lord Tyranus". He also calls Darth Vader "Lord Vader" in "Episode III". Lord Vader was actually STILL an apprentice at the end of "Return Of The Jedi", just before he turned back to the Light. He was nonetheless, a Dark Lord of the Sith, and is referred to as Lord Vader repeatedly throughout the series.
(2) Even Apprentices carry the title "Dark" Lord Of The Sith. This was not always the case. It is in the time of the two trilogies. This has been verified! Apprentices are not just Lords Of The Sith, they carry the full title, including the word "Dark". Please do not send references to novels that take place before "Episode III". At the time "Episode III" takes place, the rule has changed. This is documented at the official Star Wars web site, starwars.com.
(3) If you answered four, because Greivous is a Sith Lord, please do not send a correction; he is not, I promise. He is the only non-Jedi non-Sith to wield a lightsaber in combat in any of the six movies. Being trained in the Jedi Arts is not the same as being trained in the ways of the Force or becoming a Sith. The Jedi Arts merely refer to hand-to-hand Jedi combat techniques, specifically with regard to light sabers. Interestingly, Han Solo (another non-Jedi non-Sith) uses a lightsaber in "Episode V", but he uses it to slice open the belly of a taun-taun, not in combat.
(4) Darth Plagueis being mentioned DOES NOT mean he APPEARED in the movie!
PLEASE DO NOT MAKE IT NECESSARY TO ADD A #5 TO THIS LIST! (Legitimate corrections are welcome, but this question really is a dead horse!)