When Charlie and Dr. Hobart put one hand on Ross' face, they bring those hands together and they interlock fingers, then the camera changes positions and they interlock fingers again.
Ross' grant application is judged by Charlie's ex-boyfriend Dr Hobart, who tries to force Ross to break up with her as a condition of receiving the grant. In real life, to avoid exactly that sort of abuse, research grants (whether privately or government funded) are anonymous: reviewers never know who wrote a grant application, and applicants never know who the reviewers were, precisely to avoid that sort of conflict of interest.
During Dr. Hobart's questioning, he asks Ross what Shirelles' hit song from 1965 was later covered by a famous British invasion band. The answer to this question is "Baby, It's You", that was covered by the Beatles. However, "Baby, It's You" was released in 1960, and its Beatles' cover was released in 1963.
When Joey goes to show his commercial tape, he puts the tape into the VCR, which then ejects the tape, and still the commercial starts to play right away.
The "snacks" that Rachel gives Emma (and Joey) in the coffee shop are just boxes of Sunmaid Raisins with the logos mostly covered by gold stickers.
As per Joey, his lipstick commercial "only played in Japan". However, in the commercial, he says "lipstick for men" in English. Twice.
When Emma gets fussy while Rachel is reading to her, she says "Mama", but her mouth is shut when she says it.
As with all the work-centered story lines concerning Joey playing Dr. Drake Ramoray on "Days Of Our Lives", that soap opera films in California, yet Joey and his friends are living in NYC.
If Dr. Hobart wanted to intentionally sabotage Ross off by asking him questions unrelated to paleontology he wouldn't have asked them in front of the other applicants because they can attest to his questioning.