When Sheldon gives the envelope to Missy, it is evident that the envelope is not sealed. When Missy turns the envelope over to open it, she has to rip it open, as if it were sealed.
When the family is watching The Devil in the Dark (1967), the VHS slipcover sitting atop the television is from the 1993 VHS release, while the setting of the series is the 1980s.
Sheldon says he would "...teach you all about the ENTOMOLOGY of the word loophole..." Entomology is the study of insects while ETYMOLOGY is the study of the origin of words. As a child genius, Sheldon would know the difference and not make such a mistake.