The young Hammond in 1969 has brown eyes, but General Hammond in the present has blue eyes.
When entering Albuquerque as prisoners in the back of the blue van (11 min, 45 secs), the road is dry when the tire blows out. When the airmen get out to change the tire, the road is wet from rain. Seconds later, when the airmen start fixing the tire, it's no longer raining and the road is completely dry. Moments later, when the large military truck arrives, the road is wet again. When Colonel O'Neill jumps in the back of the truck, it's sunny and the road is dry again.
During the driving montage, SG-1 and their hippie companions pass through Chicago, which is signified by a flash of a completed Willis (nee Sears) Tower, of which construction did not begin till a year later in 1970.
The newspaper headline says that Richard Nixon would vacation at the "Summer White House". During Nixon's term, the Summer White House was in Key Biscayne, Florida. However, Nixon actually spent most of August 1969 vacationing at the "Western White House", his private residence in California.
After the military arrests SG-1, all four members are placed in one holding cell. Being a woman, Carter would be placed in a separate cell.
In the Washington, DC warehouse scenes set in 1969, you can clearly see the Seaforth Highlanders of Canada heraldry and battle honours on the far wall, indicating that the scenes were filmed at the Seaforth Armoury in Vancouver.
When SG-1 is releasing the clamps on the crate door to expose the Stargate, there are no corresponding hasps on the outer frame.
When they are supposed to be in New York, they drive up to a building with a sign identifying it as the Gordon MacMillan Southam Observatory, which is in Vancouver, Canada.
At 14:34 when they're talking to young Hammond, instead of Jack saying 30 years from now, since they're in the past, since Hammond decided to give the note, Jack says 30 years ago.
An accident sends SG-1 back to 1969. While traveling to New York, they pass through Chicago and the Sears Tower is seen in the skyline. Construction of the tower began in 1970 and wasn't completed until 1973 when it opened to the public.
The main action takes place in 1969, but the M-16s that the guards have are loaded with 30-round magazines. 30-round magazines were not issued until 1970. They should have used 20-round magazines in 1969.
Two anachronisms obvious to anyone who lived in the period. The girl says "I SO relate to that." That expression - that use of "I SO [something]" was not around in the 60s at all. It is a 90s turn of phrase. Also, Carter's "hippie" skirt is bell-shaped, with swirling patterns. Neither was even close to being a hippie fashion style. Skirts were A line or straight, and the swirl pattern is, again, a product of the 90s.
As the Stargate team travels east, Route 66 road signs are periodically shown to mark their progress. However, by 1969, Route 66 had been eclipsed by the interstate highway system.
The story takes place in August, but the cheery blossoms in Washington, DC are shown in bloom, which occurs in spring.
The signs on the highway show SG-1 traveling down East Route 66, but during the first cut to the map it shows them on Interstate 40.
When being interrogated, Col. O'Neill says that his name is "James T. Kirk of the Starship Enterprise", and the man interrogating him seems oblivious to who James Kirk is and, in fact, calls O'Neill "Mr. Kirk" several times thereafter. Given the year is 1969, and Star Trek ran from 1966 through 1969, it seems unlikely that the man interrogating O'Neill would not recognize the name and accept it as O'Neill's real name.
Daniel is supposed to be a language expert. However, when he is speaking in German to Catherine, he repeatedly says "dein Father". He should be saying "Vater" instead of "Father". He is also using the informal "dein", which is only used between friends and relatives when he should have been using "ihr", which is used in formal situations.