As Wanda is searching her phone for information on Elizabeth Frankenstein, a quick shot suggests that the Frankensteins were affiliated with some corporation named Shelley. This is a direct reference to Mary Wollstonecraft Shelley, who wrote the original story.
The character who attempts to autopsy the monster is named Dr. Pretorius. This is a nod to the film Bride of Frankenstein (1935) which has Doctor Septimus Pretorius as the main antagonist pushing Henry Frankenstein to continue his work.
Closed captioning on the film gives away the climactic discovery of the monster's, that he has a name.
The idea that a created body would be riddled with cancers actually has historical precedent. Attempts at de-extinction have tended to fail because cloned cells have difficulty with replication, which is basically what happens with cancers. The first successful attempt to bring back an extinct species in 2003-the bucardo, a species of wild goat-did not live long because of tumors.
The MPAA number at the end of the film (#47714) is the same on both "Frankenstein" (2015) and "The Place Beyond The Pines" (2012).