Not all mistakes are created equal. A Peach getting hit by a soft Sheik b-air while on a platform and taking needless damage is an error. Messing up a powershielded laser against Falco is another error. They cost you a bit of percent, but they generally aren't that big of a deal.
On the other hand, missing a tech against a Pikachu on FD when you're playing as Fox is a HUGE mistake because he's going to CG you from zero to death. Letting Puff u-tilt you at 10 percent without CC'ing it is big mistake. Falco burning his double jump somewhere, then finding himself beneath the edge of the level is a massive mistake. These are the kinds of errors that will cost you an entire stock in the blink of an eye. So, to repeat: not all mistakes are equal.
Look at this from two perspectives. First, as a player, your goal in a match is to AVOID those critical mistakes. Knowing the matchup that you're playing is pivotal for this reason, because it tells you what mistakes are huge, earth shattering, game costing errors, and which ones are not. And that will generally give you information about how you should be playing your matchup! You can also learn ways to reduce certain openings and minimize damage on you; CCing, DI'ing combos so they can't land efficient finishers, and just staying in positions where your opponent can't land combo starting moves. It's an underrated defensive skill, but minimizing damage to yourself is something a lot of good players have. It's why you don't see them get hit by lots of stock ending combos; not just because they don't get hit, but because they are good at minimizing damage through intelligent decision-making.
Second, your OPPONENT will be making these mistakes as well. Knowing what they are and knowing how to capitalize efficiently can make you a nightmare to play against in those matchups, because it creates an ever-present threat that any mistake can end the stock. M2K's Marth against Fox or Falco, for instance, is one of the most shining examples of this. He practically earned a living by chain grabbing, comboing, and gimping spacies off the most inoccuous of hits. Of course, this earned him a reputation for "playing gay," but when you get right down to it, every player wishes they could be as efficient at murdering Fox and Falco as M2K was. It meant that every match against him was close, even if you were 3 stocks ahead, because you were always a few mistakes away from losing the game. So not only is it a skill to see these mistakes and capitalize, but it's also a skill to convert smaller errors and openings into bigger ones with good resets and reads.
Remember, your job--and your opponent's!--is to turn every hit into a stock when possible. Likewise, you also must avoid letting little openings snowball into bigger ones, and learn how to read when your opponent is going for big punishes so you can dodge them.
Sometimes stock-ending decisions can just come from a really solid read. They aren't necessarily mistakes, but simply positions where certain options have nasty consequences if the other guy guesses right. In this video: http://www.youtube.com/watch?v=3qwKHr-5wyk#t=6m59s
I hit ARC with an f-smash, and read his up+b to the edge, and just go for an edgehog at 54 percent. It's not really an error on his part; getting the edge is an excellent idea for spacies, and up+b'ing high can give them lots of recovery options. But if you can get the read in a critical situation like that, you can take stocks without even touching the other guy. Then my next stock on him is him allowing the ICs to land a synchronized grab near the edge, then not escaping the d-throw d-air, two pretty big errors for a space animal to make in that matchup.
One of the nice things about landing these critical hits is that they have a tendency to send the other guy on tilt. It gets him thinking that you got lucky, that the matchup is stupid or lame, and that can lead to hasty thinking that lets you exploit more of these nasty mistakes. And again, the flipside is to understand that every matchup has these and it's entirely possible you may fall victim to them, and shake it off when it happens.
So, how can you get better at seeing these situations and capitalizing? Here are some general tips:
--if you have a chaingrab of some kind, you should spend some practice time trying to link your hits--even really stupid, lame, lucky ones--into grabs. Resist the urge to go for smash attacks as your finisher, and try to look for ways to extend your combos.
--if you have the option of sending someone off the edge, consider using weaker hits that will send them low, rather than a more powerful one that lets them DI upward.
--if your opponent really likes going for the edge, give them a little time to decide they're going to go there, then just take it from them.
--if your combo can either keep going or you can end it, mix it up! For isntance, a badly DI'd knee from Falcon can end the stock on a lot of characters at 40 percent, and if they're certain you plan to go for up-airs instead, you can cheese out a stock off one powerful hit.
Remember this and learn how to spot those really big mistakes in the blink of an eye, and soon you will need to go on a diet from eating too many free stocks. Good luck!