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.
Children of Earth: Day One - S3-E1
Character mistake: Lois says that Colonel Aduya's uniform "isn't British Army". In fact, it is entirely (and accurately) British Army with the exception of the small UNIT badge over the pocket.
God Is in the Details - S2-E10
Character mistake: When Diane quotes the scripture, she says "Revelations." However, it's just "Revelation." Someone as smart as her who has read the New Testament (or heard it quoted) would know the correct word.