Inspired both by the realization that while I don't have a Maine accent, my speech features much idiosyncratic "Maine vocabulary", as well as by my ever-present fascination with linguistics, I've been reading up on the Maine accent a lot lately.
Among other things, I've found that one of my private theories about the origins of the accent is actually generally held in linguistic circles. This theory is one that I've expounded on at length to many people, but I'll summarize it again here: the dialectic traits of the Maine accent seem to draw more directly from features of colloquial British English. The primary similarity lies in the common predominance of "R-drop phonetics", although the ways the vowels surrounding these dropped "r"s are pronounced vary considerably between the two types of dialect.
Here's a neat article I found. Not the most scholarly article(in the sense that it doesn't talk a lot about rhotic tendencies in dialects, or nasal vowels, etc) but a good analysis and fun to read.
The Maine accent is nothing short of fascinating, if you ask me. It would also probably be a field day for someone studying linguistic origins in America, since every town seems to have very slight variations on the accent. In some of the more isolated areas, people came over from England back in the 1700s and have been fairly insulated against population ingress over the last 3 centuries, so their accent is almost closer to the proletarian British accents than to standard American.
This, of course, is mostly limited to very rural areas, and even in such places the accent is disappearing faster now than ever before, as more rural areas fall victim to sprawl and artists and such from away (another very Maine expression) take up residence and "dilute" the accent, if you will. The more standard "New England accent" or "Boston accent" is observable both in the city of Portland and in points south towards New Hampshire and Boston, though the majority of people, even those who grew up in this area like myself, speak basically the same as the news anchors on CNN.
Obviously, I can't really explain the mechanics of an accent via the internet. A good way to get in the frame of reference for trying imitate this accent, however, is to pronounce the word "mash" as most Americans would pronounce it, but imagine that you are actually referring to a marsh, that is, a piece of wet, swampy land, when you say it. Now, while you're in this mode, imagine your lobster boat has been grounded on the dock for repairs, and your 400 hp Evinrude outboard motor has just toppled out of the engine well and into the brine beneath. Now, contort your face ever so slightly and say "Well, hadn' counted on that now..." Some accents are easy to recreate (like the Brooklyn accent), but this one is near impossible to pin down.
There's also a store in Portland (where, of course, this accent is virtually nonexistent) called "Queen of Hats". The store sells hats. Do you get the joke yet? Well, I think saying downeast Mainers would pronounce "heart" the way more Americans would pronounce "hat" is a bit of a stretch. They would probably hit the "r", especially in places where the accent is bit more rhotic.