Body Repair Shop
In both the 1973 film and the TV show, Hosts are repaired in hospital-like settings. Employees are dressed in scrubs and perform surgery on the hosts.
Westworld in the TV series operates similarly as Delos in the film. Guests are able to do anything they want with the hosts, guns are unable to harm guests and hosts are forbidden from killing guests. One difference is that in the film, hosts are not allowed to harm guests, while in the TV series, hosts are allowed to harm guests that have paid a premium.
In addition, like Delos in the Westworld Film, Delos Destinations, Inc. runs different themed parks near Westworld.
The Gunslinger on Sub-Level B82
Whilst looking through Sub-Level B82 Bernard's torch briefly illuminates The Gunslinger, from the 1973 film Westworld. The figure seen in the episode is a statue, made by Nick Marra. There's a link to his (delighted) instagram post on the subject here
In "The Original," Ford mentions that "a simple handshake" would give one of the early hosts away; in the Westworld film, androids could be identified by their hands.
William and Logan
William and Logan have some similarities to Peter Martin and John Blane respectively. (Young) William, like Peter, is a first time visitor to the park, while Logan, like John, serves as a guide to William. Peter was also recently married to a woman named Julie, whereas William is engaged to be married, to a woman named Juliet.