Western Electric phones, like the 500, 554, 2500, 2554, Trimline, etc., are what most of us who grew up in the '80s or earlier are familiar with, because Western Electric was the Bell System's (AKA: the original AT&T, AKA: Ma Bell) manufacturing arm, and since most people had phone service through the Bell System, and the Bell System didn't allow third-party equipment to be hooked up to their lines, they had to lease their phones from the Bell System, and those were all Western Electric phones.
Back in those days (prior to the court-ordered breakup of the Bell System in 1984), you generally couldn't/didn't just go to the store and buy a phone; you leased your phone through your phone company, which for the vast majority of Americans was the Bell System. However, for people who got phone service through one of the various small independent phone companies at the time, they didn't get Western Electric phones. They got licenced clones of Western Electric phones from companies like ITT or Stromberg-Carlson, or original designs from e.g. Automatic Electric.
So back then there was no legal path to ownership of a genuine Western Electric phone (they were all marked "Bell System Property, not for sale"; this changed in 1984), so it would make sense for prop companies to buy phones from other manufacturers rather than deal with Bell System-owned Western Electric phones. Also, Hawaii was in GTE territory, rather than Ma Bell's, and they used Automatic Electric phones (as well as owning Automatic Electric itself).
One of the ways to identify an Automatic Electric phone with regard to a traditional rotary desk phone (in the style of a Western Electric 500) is to look for a ridge along the back of the handset:
If you can get a close look at the base you can notice other differences, like the shape is more rounded, the two forward posts of the handset cradle are truncated, along with various other shape differences, and there are triangles under the holes in the finger wheel rather than dots. This is like the black phone on Higgins' desk (AE-80 or AE-80e; can't see the front of it in that shot), and the red Robin Masters phone is an AE-980/AE-981 Styleline, which was Automatic Electric's answer to the Western Electric Trimline:
There were also some weird Automatic Electric phones on the show that looked like a cross between a Western Electric 500 and a Western Electric 2500 (i.e., like a 2500 with a rotary dial), like this one (AE-80e):
There were plenty of 2500-style phones too, which was a Western Electric design that was (and still is) cloned by many manufacturers. GTE / Automatic Electric's version was what was used on MPI, and was also an AE-80e (Automatic Electric's model numbers were the same for a given style of phone regardless of whether it was rotary dial or touch-tone). Magnum's desk phone in the guest house ...
... was an AE-80e:
Note the truncated front posts of the handset cradle; this readily distinguishes it from a Western Electric 2500.
Magnum's kitchen phone in the guest house ...
... was an AE-192:
The wall phone that was used to talk to people at the gate and let them in ...
... was a Radio Shack Duofone 16:
The two lights above the keypad may have been added by the prop department, though I suppose it is possible for the phone to have come from the factory that way, or have been modified by a telco (they are merely visual indicators of the phone ringing; two of them suggests a 2-line phone).
