Continuity mistake: When Kyle is taking the test, he's doing it with precision and accuracy, but he marks the wrong answers for #31-33. Even though it's meant to be a continuous shot, when he's answering #35, his answers to #31-33 are now changed to the correct answer. Kyle is able to answer the questions right the first time and didn't go back to change his answers, plus there's no sign of the previous marks if they were erased.
Character mistake: When Kyle is re-taking the test at the end of the school day, you see him bubble in 4 answer and turn the page and continue to answer questions. However there were 7 questions on the first page so he ended up putting the answer to #8 on #5 of the scantron. Kyle is too smart to do this.
Revealing mistake: When they shine light through the Zyzzx ring, Kyle walks in front of it, but the map is still visible on the wall. Meaning that it's either added in editing or the light shines from another source.
Answer: Yes, he is the one wearing the Fedora Hat. Look for him in Season 1 Episode 4.