Stargate SG-1 Factions

Another aspect I must include is the little things that tie Stargate: SG-1 with Stargate: Atlantis. Some people suggest that you watch them as they originally aired with Seasons 8-10 airing in conjunction with Seasons 1-3. Some have even suggested to watch each season in sequence with Season 8, Season 1, Season 9, Season 2, Season 10, and Season 3. I personally feel this wasn't necessary. There are very few tie-ins between the two series. One could argue that you should be familiar with certain characters and setting before watching Stargate: Atlantis. I could also make a parallel argument that it is necessary to understand certain races of Star Trek: The Next Generation by watching Star Trek: The Original Series. However, the main plot and setting is completely different.

Neither the conflict with the system lords or the Ori show up in Stargate: Atlantis. In fact, only one episode brings in a Gao'uld. What I did notice was little things that foreshadowed the series. What were these?

Sound Effect: SG-1 Season 2 Episode 6 reveals the true identity of the Asgard (as little gray men), their ships, and their ability to pull items away from the planet. This is perhaps the only moment the distinct "culling" sound is heard that the Wraith use in Atlantis. On many occasions, they use their teleportation device to withdraw items from the surface.
Asgard: SG-1 Season 5 Episode 10 reveal that not all Asgards died when their planet exploded in the SG-1 finale in Season 10. However, the very rushed ending of them dying and the tacked-on "secret" mystery of the Asgards being behind the team's kidnapping were both sudden and unexpected. The characteristics of the event and race are far too different to need a previous viewing.
Replicators: Season 3 Episode 5 of Atlantis reveal a more humanoid evolution of the Replicators first seen in Season 6 Episode 12 of SG-1. Although similar, their origin is well explained and may or may not be directly tied to the "toys" seen in the SG-1 series. The Atlantis crew do make use of the ARP technology Jack formed in Season 8 Episode 2 of the series.
Ascension: One of the earliest critical moments of the Ancients ascending to a higher plane of existence is in SG-1 Season 5 Episode 3. This played a huge portion over the rest of the Stargate Mythology in the series. Without knowing a lot of the little details, one could easily get lost and confused when most of the lore is dumped in Atlantis Season 1 Episode 14 when they discover one of these beings. The writers did their best to bring one in without any previous knowledge of the other series.
Gao'uld: Season 2 Episode 13 brings in SG-1 with an evil Gao'uld spy that messes up the Atlantis crew. Honestly simply by watching the original Stargate movie one could understand this concept. This is the only instance I recall that one shows up.
Characters: Season 5 Episode 14 and Season 6 Episode 1 shows early on one of the Atlantis crew members - Rodney McKay. Season 7 Episode 21 through Season 8 Episode 2 shows off Elizabeth Weir (ironically played by two different actresses) that leaves and officially leads into the Atlantis series. Richard Woolsey is first shown in Season 7 Episode 18 among a documentary crew and doesn't play an active role in Atlantis until Season 3. Many others, including Samantha Carter and Daniel, pop up in Atlantis eventually.
Wraith: The only instance of the Wraith showing up on SG-1 series is a very brief moment in Season 10 Episode 3 where they destroy an Ori and Wraith ship at the same time. The Wraith ship only appears on screen for a couple seconds before it blows up.