I always thought Alaskans sounded a bit Canadian. The sum total of my experience with Alaskan speech comes from Deadliest Catch, though.
I have a friend who grew up in the same place as me (central California) and had the very, very light southern accent we have here, mixed with the sing songy normal So Cal way of speaking. About 6 or 7 years ago, he moved up to Alaska and actually lives not too far from Wasilla. He definitely has picked up. . . some sort of accent. I can’t pin it down, but when we talk on the phone now, there have been several times where I’ve started laughing at him for sounding like Sarah Palin. Don’t get me wrong, it’s not nearly as pronounced or obnoxious as her way of speaking, but just the way he enunciates certain words. . .
The unrevived thread predated Palin’s national prominence, so there’s no Zombie Palin involved.
Alaskan born and raised, me. Linguistic background: I am tested high-aptitude for languages and have spoken four languages fairly fluently in my life. I am also a good mimic and have an ear for dialects and accents.
I left Alaska at age 20 and returned to live there at age 50, with several visits in between. After a 30 year absence, I’m sure I would have detected an accent, particularly from my family members who remained there all that time and from co-workers.
IME, Alaskans with accents fall into three categories: Alaska Natives, immigrants from other states/countries and their offspring, and poseurs. There are a large number of people there who are from elsewhere, particularly since the oil boom started and Texans and Okies flooded the place. Their accents are genuine, if occasionally annoying. 
Palin is a poseur, who affects a folksy accent in order to ingratiate herself with others. There are many like her who affect a Midwestern accent, or a faux Western accent attempting to immitate a Montana drawl. Beats me why they do it.
Due to the fact that basically no one is a fifth-generation Alaskan, there hasn’t been time for Alaska to generate it’s own distinct accent. Everyone born and raised here kind of generates their own strange variant accent, based on the strange hybrid environment. If anything, it’s easy to spot an Alaskan accent, just based on how goddamn unique that person’s accent is.
I’ve lived here in Alaska for all my life, cradle to early 20s. If you want to hear my strong Alaskan accent, post up a script for me to recite.
I grew up in Alaska.
Lots of people had accents from where they grew up. There are a lot of transplants, so it’s common to hear accents from all over.
Alaska Natives sometimes have a particular accent, even if english is their first language, especially if they grew up in the bush.
Everyone else just had a generic west coast accent. To my ears, I talk exactly like people on TV talk.
I live on the west coast of Canada, and I fail to detect any significant diffences in accent between the western lower states, BC, or Alaska.
Nothing like the difference one encounters when crossing the Niagara River from Ontario to New York.
Or listening to Bostonians or Newfoundlanders.
I think it takes a couple of centuries of relative isolation to develop a regional accent, and in this day and age of television, individual group accents are even less likely to take hold.
Slight nitpick, but the Kennedys don’t have a Massachusetts accent. I guess they have a Kennedian accent.