The name of the Detective, Manacek, seems to be a combination of Mannix (1967) , who is a private investigator, and Banacek (1972) . But, the entire episode is a spoof of the series Banacek (1972) which was about an independent insurance investigator who is wealthy and a suave ladies man that solves intricate cases of stolen items.
During the montage of Homer staring at the painting, there is an Egyptian statue in its case that keeps moving in a circle from moment to moment. This is a reference to an actual statue at the Manchester Museum that was seen on the security cameras to spin around 180 degrees over night without anyone touching it.
The usual Simpsons-style credit sequences and gags are replaced with credits in the style of Banacek (1972), right down to the typeface, theme music, and shots in the opening credits of Manacek rowing a skiff and driving his classic convertible this is the first time in the series the credits are replaced.
The end of episode paid tribute to the late Stephen Hawking who passed away four days before the original air date.
After the episode aired, it was revealed that series co-creator and EP James L. Brooks hated the character of the Rich Texan so much that he personally created the Megan Matheson character in order to replace Texan in the show's story. Brooks actually advocated for killing off the Rich Texan entirely but the idea was vetoed by Al Jean because everyone had agreed not to kill off noteworthy supporting characters after the unpopular decision to have Krusty's father die in "Clown in the Dumps (2014)".