In my writing posts, I've been talking about some plotting issues, and I've noticed that a lot of plotting problems I see actually come down to character problems. It's not so much that the characters themselves are the problem, but rather that writers aren't taking characters into consideration when developing plots. But no matter how plot-driven a story might be, it's still bound by the characters. You end up with a bad plot if it requires the characters to go against the personalities that have been established or to otherwise act in a way that isn't realistic or believable.
The "Idiot Plotting" I referred to a few posts ago is a subset of this -- in order for the plot to work, the characters have to lose all common sense or knowledge and act like idiots. It's not restricted to idiot plotting, though.
In court cases, they often talk about the "reasonable person" standard -- would a reasonable person believe this or act this way? That standard also applies to fiction. Would a reasonable person respond this way? Too many plots crumble because they require characters to behave in a way no reasonable person would. They trust someone who's sending off massive "don't trust me" signals, they forgive too quickly and easily for the harm that's been done to them, they panic or refuse to panic in a way that doesn't fit the situation. I also see this in conjunction with the Mary Sue problem I mentioned before, with the other characters not responding to the Mary Sue in a way that normal people would, either loving her in a way that doesn't match her actions or hating her unreasonably so she can be a misunderstood victim who'll show them all.
Or there's the characters suddenly losing their characterization in order to make the plot work -- the cautious to the point of paranoid person suddenly trusting someone, the rational person panicking, the adventure seeker walking away from danger, etc. The more three-dimensional and well-established your characters are, the worse this problem is because your readers will know these people would never do these things.
The best way to avoid this is to make a point of considering what your characters would do as you develop your plot. Or, if you plot first, reverse engineer your characters to fit the story you've developed so that in other parts of the story they're behaving consistently with the ways they behave in plot turning points. If you need a character to do something to keep the plot going, you need to establish that either that's something this person would really do or something they might do in that particular situation. Lay the groundwork by showing the tendency or trait earlier in the story or show why this one situation is different. People have weaknesses and blind spots, and even someone fairly rational may have that one thing they're not rational about.
This also applies to the "reasonable person" problem. Even generally reasonable people have their non-reasonable moments. You just have to provide the proper motivation. The more unreasonable you need someone to be, the stronger the motivation has to be or the more extreme the situation. If you need people to panic, you need to give them something likely to make them panic. If you need them to not panic in a panic-worthy situation, you need to hide some of the bad info from them or give them an experience that makes them think maybe this situation isn't so bad. You can also establish that this particular person isn't a "reasonable person" by showing elsewhere in the story that he always reacts in ways you wouldn't expect him to. That way, when it becomes critical to the plot, the reader is saying "There he goes again" rather than "Yeah, right."
As with so many plot issues, the place to fix the problem may be elsewhere in the story rather than at that critical point. It's not so much the critical point where you need to make changes. What you need to do is set up the critical point in a better way.