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At the beginning of the episode, SG-1 returns early from a mission. Then, a few minutes later, another SG-1 returns on schedule from the mission. General Landry and the two SG-1s quickly figure out that the first SG-1 team that returned is actually from an alternate universe. (I'll call those characters Mitchell-1, Teal'c-1, etc.) The second SG-1 team, that returned on schedule, is the genuine SG-1. (I'll use the regular names for them.)
Although the SGC is aware of the existence of alternate universe (such as from season 1's "There But for the Grace of God"), they know of no reason why an SG-1 from an alternate universe would come through their stargate. The only indication of something amiss was a strange flash of light and burst of noise when their wormhole connected to the stargate. The other SG-1's universe is extremely similar to our own, but there are some differences, such as the fact that Jacob Carter and Selmak are still alive.
General Landry and the "real" SG-1 begin questioning the alternate SG-1 to ensure that they really are from an alternate universe and not some type of impostors. The alternate SG-1, on their part, are suspicious that they might not really be in the SGC, but that they are being manipulated by aliens (a la season 2's "Out of Mind"). Carter and Carter-1 begin discussing how the connection between the two universes could have been made, and they finally decide there must be some involvement by a black hole, possibly the one that was created by the Ori in "Beachhead".
The alternate-universe hypothesis is confirmed when another SG-1 team arrives from yet another alternate universe. Landry orders all other SG teams to head to the alpha site, and notifies other incoming alternate-universe SG-1 teams that he will not open the stargate iris, unless they are in under fire. (This is the first sign that there is any confirmation sent to the off-word SG teams that the iris is open and they are safe to come home.) As he says, "I'm not about to turn this base into the Grand Central Station of the multiverse!" Despite his restrictions, he allows at least 16 alternate SG teams to travel to the SGC and has turned back over 50 teams; apparently they are not all SG-1s. Some of the teams include people that have died in the "real" universe: Martouf and Dr. Frasier.
From a suggestion by Carter-1, Carter develops a plan to stop more alternate-universe SG teams from arriving at "our" SGC. The plan involves using a specifically-shaped explosive device to seal the inter-universe breach (similar to the plan from season 2's "A Matter of Time"); they will use an Asgard time-dilation device to get the explosive device to the black hole from the Ori beachhead in a reasonable amount of time. The down side of this plan is that all of the alternate SG teams will be trapped on Earth. Nevertheless, Landry approves the plan.
The first alternate SG-1 team accompanies SG-1 on the Prometheus to deliver the explosive. Once the ship is underway, the alternate SG-1 captures the real SG-1 and changes course for Atlantis in the Pegasus galaxy. Carter deduces that the alternate SG-1 planned and instigated this whole series of events: they figured out how to make a breach between the universes, then played dumb about it to guide events to their current state. They are now planning on stealing Atlantis's ZPM and returning it to the Earth in their universe in order to power the Ancient defenses in Antarctica, because their Earth is under imminent threat of an Ori attack.
With some clever double-crossing, the real SG-1 regains control of the ship. Carter has realized that they can use the alternate SG-1's method of causing the breech in the first place to send the alternate teams back; she has also realized that this can be done from Earth, so they return to the SGC. They detonate the explosive through an open wormhole, which reverses the direction of the inter-universe breech. Then they dial each of the alternate teams' point of origin, and send them back. The SG team with Martouf and Dr. Frasier is the last to leave, and General Landry sends with them some of the Prior plague vaccine, which should help them combat their own plague. End of story!
The basic premise for this story - lots of alternate-universe SG-1s come to Earth - is really pretty weak. The supposed scientific explanation for how the alternate universe travel was caused was very thin, even for such a speculative subject. It really felt like an excuse to have "reunion hour on Stargate SG-1". Even in other alternate universe episodes, such as season 1's "There But for the Grace of God" and season 3's "Point of View", there was more of a goal to the episode than just "fun with alternate universes". This really brought the episode down, in my opinion.
I also didn't much care for making the first alternate SG-1 responsible for the inter-universe breach. First, it's hard to believe that they actually a plan involving going to an alternate universe to look for a ZPM would work (although I suppose our own SG-1 traveled through time for the same goal in season 8's "Moebius, Part 1" and "Moebius, Part 2"). It's also hard to believe that an SG-1 team made up of people we know would agree to such a plan because of the possible harm it could do to the people in the other universe. However, this point is made somewhat more believable when the attitudes of the alternate SG-1 become apparent when they take over the Prometheus: they seem incredibly smug. Teal'c-1 gets "satisfaction" out of slamming Mitchell's face into plumbing. Mitchell-1 and Carter-1 both wear self-satisfied smirks when their plan is enacted. Although Mitchell says that they aren't wearing beards, so they can't be from the "evil twin universe" (from the classic Star Trek episode "Mirror, Mirror"), the alternate SG-1 members certainly seem to have different morals. Perhaps they are just desperate, but if that was the case, I wouldn't expect them to be smug.
Our SG-1 defeating the alternate SG-1 in the end felt weird: it's odd seeing any SG-1 team not succeed. I was surprised that the alternate SG-1 didn't make any more attempts to break out and continue with their original plan. After all, our SG-1 wouldn't give up for anything. Maybe it was too late and the alternate Earth had already been attacked by the Ori?
Despite the contrived nature of the plot, I will admit to some guilty pleasure in seeing some characters return and hearing about the lives of the alternate characters. Carter's love life in particular gets a lot of play: in one universe, she just had her honeymoon, in another universe she's on maternity leave, in yet another she had a relationship with Martouf, and so on. When Martouf does arrive, he and Carter naturally become close again, although one might wonder why Martouf chose "our" Carter to get to know instead of one of the 16 others. Fortunately they realize that they are not actually the people they desire, despite appearances, and they don't get too attached.
Carter also gets the most visual humor. The scenes showing a roomful of Carters are humorous, with all the varied hairstyles and dress. It also appears that the Carters in all universes are fond of the base cafeteria's jello.
I will say that I definitely enjoyed seeing Dr. Frasier again. The scene between her and Daniel and Teal'c as the two men are amazed to just see her is touching. In Frasier's universe, she is trying to find a cure to a Prior plague; when General Landry tells her she may be stranded forever, she gives him a strong dose of her characteristic righteous indignation, asking him what gives him the right to choose to save the people of his Earth over hers. There's been no character since her death that was willing to clash with the general this way. The closest character, Dr. Lam, is usually too busy either being annoyed by stupid military rules or angsting over her father being a dope. I wish we had seen Carter and Frasier talk more.
With all the possible alternate universes and SG-1s that we saw, I felt like there was one obvious omission: O'Neill. Surely one of these alternate universes still had a General O'Neill that might have been accompanying a mission, or even a Colonel O'Neill who was still leading SG-1? I missed seeing him... and heck, the writers could have used this as an excuse to give Carter's love life another permutation.
One more interesting character from "our" universe was introduced: the Asgard Kvasir. He was pretty funny, although I'm sure he wouldn't have understood why! He clearly has a lot of doubts about the abilities of humans and almost couldn't bear to let the time-dilation device out of his sight. His speech about needing "courage and a steadfast resolve" before making a hasty exist was great.
Well, that might be all of my comments. This was quite a fluff episode, and didn't serve to advance much of the overall story. It also didn't show us much more about our characters, because nearly all of the new stuff we learned about them was about the alternate universe versions of them. While it might show possible paths for the characters, it's by no means definitive.