An interesting question asked by Leverage's John Rogers in this blog post (which itself spins out of an io9 post): When should newbies stop watching Battlestar Galactica? Here are some of the answers he received.
"One Year Later" (end of S2, don't even finish the scene, just shut it off when you see those words).
[I]n the final episode, when they start discussing city planning. That leaves out most of the stupidity.
If I was giving the box set to a total virgin, I would suggest they stop watching right away and go get Season One of "Doctor Who" instead. And I'd keep the receipt.
[T]hey should stop about five minutes from the end of the finale, in the middle of Lee and Kara's conversation. (But if they want to fast-forward through the love pick-a-polygon crap in season three and Kara's crazy time in season four, that's fine.)
Just to offer a somewhat different perspective, I'd advise somebody to watch it until the end, unless they started not enjoying it. I thought the first two seasons were stronger than the second two seasons, sure, but unlike (apparently) a lot of people I didn't experience a precipitous drop-off where things got worse and worse. Just about every step along the way made sense to me as a creative choice, and played honestly with what came before.
As opposed to, e.g., Alias (which was obviously a very different, and incredibly less ambitious [and artful] show), where I tell people they should check out the first two seasons and then immediately stop. Sure, the first episodes of Season 3 seem acceptable, but the nuttiness and badness just start expanding at frightening speed.
It's potential snark heresy, but I agree with the last of the comments; I know that the finale was nowhere near perfect, but I genuinely think there's value in BSG all the way until the very end. Well, maybe not that montage at the very end, but still... I open the question to everyone here, though: When do you wish you'd stopped watching the show?