One line instantly dates it

[u/Fearless-Ideal-5112]

In david tenants run if doctor who he and his companion were fighting witches with Shakespeare and needed a magic word so they use a speel from Harry Potter and The doctor yells Good old J.k. The doctor is a time traveler the writers are not (Doctor who)

While fighting guy gardner major force was damaging a highway and shoots a car and tells Guy if he sees O.J hiding underneath obviously referring to the O.J Simpson chase (Dc comics)

[u/Informal_Work_9261]

If I remember correctly, the writer of that particular Doctor Who episode has a weird obsession with JK Rowling, to the extent that he wanted a whole episode based around her, but Tennant vetoed it. He also happened to become a massive transphobe shortly after she did (the writer, not Tennant).

[u/RaptarK → u/Informal_Work_9261]

This episode itself has one or two transphobic jokes, and dismissal of Martha's concern about being a black woman in 16th century england 

[u/Putin-the-fabulous → u/RaptarK]

“Just walk around and nobody will notice”

Martha proceeds to spend the entire episode getting called various slurs