The biggest things for affecting accents are knowing what your own voice can and can't do -- it's like learning an instrument, to some degree -- and paying attention to how things
sound. Most folks just listen to grasp what the words being said mean, rather than also paying attention to how the sound.
That being said, I've always been fairly good at picking up accents. Growing up I had a scoutmaster for some time who was British, he and his son both had fine accents. I had to consciously prevent myself from slipping into one when I was around them, kind of a verbal chameleon effect.
The accents that gave me the roughest time for a long time were the Irish and Scottish accents. I could do the Scottish relatively well fairly quickly, but the Irish one gave me fits. I could tell them apart when I heard them, but I couldn't get hold of the Irish one enough to actually replicate it.
I find Russian and Scottish the most fun to play with. Though I haven't been around Russian accents nearly enough to distinguish the various flavors of them.
Well, if you want to get into word misuse pet peeves, my biggest are imply and infer -- folks can't seem to get them straight. For those who don't know: imply is what the speaker does, infer is what the listener does.
The one I've been running into recently is misuse of juxtapose. Again for the uninitiate: it is
not a stronger way to say "oppose." That's the way I keep hearing it misused: "So and so is totally juxtaposed to such and such." To those who know the word means "placed side by side," the speaker sounds like a doofus, because what he's saying is the
exact opposite of what he
means to say.