Crew or equipment visible
Errors in geography
This type of modem cannot make phone calls on its own, because when the handset is physically removed from the phone it immediately connects to a dial tone, and the only way to hang up is to physically press the button on the phone base or replace the handset.
The first time the modem is used in the movie you can see how it really works: David picks up the handset, and he manually dials the school's phone number on the phone base, then he places the handset in the acoustic coupler so the modem can connect.
The goof is that war-dialing, which is where David had his computer call long lists of phone numbers one after the other, is not even possible with his modem because the phone cannot be physically hung up between calls to make the next call (you can clearly see the handset on the acoustic coupler when the war dialing is going on, so he's not using some other modem). This is incredibly ironic, because the term "war dialing" came from this movie, but it was not even possible as depicted in this movie.
Further evidence that each call must be made or answered manually with this type of modem is when WOPR calls David back, and he has to manually answer the phone and place the handset on the acoustic coupler to connect.
This is incorrect for Titan II deployments. Only Minuteman missile units had a two-man crew in command of a flight of 10 missiles and the movie actual shows a Minuteman launch control center. Titan II crews were only in command of one missile with an attached launch control center and the Titan II crews consisted of 4 men in a control center layout that is completely different than the one shown.