Jackie states that Wonder Woman is from the Amazon. While she's part of a tribe called the Amazons, she lives in the mythical island Themyscira, not in the South American rain-forest.
The book Adam is reading is clearly not one of the Lord of the Rings novels. It's way too small.
Lainie says that she wasn't going to prom because of the "who Shot JR" story line in Dallas. This story line was in 19080; however, in this episode the character of Matt Bradley is present and he became a member of the JTP in 1987, as evidenced by the use of the song Touch of Grey in the episode in which Matt met Adam. Therefore the Who Shot JR storyline was not playing on Dallas at the time.
When Jackie is laying on her bed while Adam's voiceover says, "I had lied to the geeky girl of my dreams. I knew the only way to win her back was with a grand gesture", she is seen playing a Nintendo GameBoy. Episode continuity suggests that this scene was meant to be sometime earlier than June 23, 1989 (based on references to the 1989 Batman movie in the following episode). As the Nintendo GameBoy was was not released in North America until July 31, 1989 it would be highly unlikely that Jackie would own one.