the psp is nowhere near a mistake.

The original Game Boy did sell fairly well, and came close to matching the NES' sales before it was finally discontinued and replaced with the Game Boy Pocket. From 1991 to 1997, however, it had the Game Gear competing against it. In the peak years, the combined hardware and software share between the two hovered somewhere around 75% Game Boy/25% Game Gear, the closest any handheld ever came to overthrowing the Game Boy. Similarly, the PSP is currently hovering around 25% hardware/software-combined market share to the DS's 75%.

Sega jumping their own "Saturnday" launch party by selling it in "a few select stores" months earlier by surprise, alienating many (including Wal-mart), without even telling most third parties and therefore ensuring that the Saturn would limp out of the gate and be hated by retailers and publishers alike.

Dropping Blu-ray out would have made PS3 resemble X360 more. Only PS3 would've been more difficult to develop games for... It might actually have been PS3's saviour.

I don't know about history too much. More recently there have been mistakes as well but I can't really think of bigger ones right now. Maybe I'll post them if I figure out some.

 Disagree with the first.

slightly disagree with the second... but I do think Wii is the worst console this gen, If and ONLY IF Microsoft gets rid of RRoD. 

so you are comparing the Game Gear to the PSP? lol

There's a lot of similarities between the two, actually. Not just in sales trends, but in design decisions and end results as well. Both relied on a "better" screen and "more" controls than their competitors, as well as a more impressive sound processor, at the cost of battery life. Both have a larger physical size and weight than their direct competition (though not by a huge margin in either case). Both have screens noted for having ghosting issues. Both were marketed as a "better option" to the Game Boy line. Both prominently featured ports from previous systems and were similar to those previous systems (the GG is basically a beefed up portable Master System; the PSP is basically a beefed up portable PS1). And both garnered less than stellar software sales (in that regard, though, Game Gear actually outclassed the PSP, mostly because pirating GG games was not at all easy in the time of its market presence).

 name me number of GG games that sold over 1 million

and answer that with PSP.

and... look at total hardware sales number.
There's absolutely no comparison.

Going by raw numbers is meaningless when comparing past to present; market expansion has been occurring for the entire span of the video game industry's existence. That the PSP is doing 3 times better than the Game Gear should be expected; everything is doing at least 3 times better than products released 10 to 15 years ago were doing. The NES was an abnormality in its time; the fact that it sold so much was unheard-of, most systems prior to and indeed during its lifespan only sold a sixth of what it did when they were absolute blockbuster successes.

1. Sega abandoned the Saturn because gamers were abandoning the Saturn. This was because they screwed up in prematurely abandonig the Genesis (and releasing various add ons for that system) which undermined consumer confidence. With the Genesis, Sega had pulled even, if not ahead of, Nintendo, and they flushed it all away. So the #1 for me has to be the abandonment of the Genesis, which led to two commercial failures and Sega's exit from gaming.

2. Nintendo didn't say "screw off" to third party developers - that would imply that they chased them away deliberately. They did alienate them, but that wouldn't have much mattered had they remained the top of the heap. The real problem was that it pulled out of it's development deal for a CD based console with Sony, which led to the creation of the PS1 (giving 3Ps the opportunity to abandon Nintendo) and thus the PS2 and 10 years of Nintendo as being the "also ran" console maker. If Nintendo had failed with the Wii, this would be #1, but since they survived and Sega didn't, Sega's blunder gets the pole position.

3. BR alone wasn't a mistake, as that capability ensured that format's success. But the entire design and marketing of the PS3, the overall arrogance of Sony, was a crippling blow to the PS3 which took a year to fix and likely will relegate them to third place for at least the rest of the year.

Compared to these, Virtual Boy is a minor issue, causing no real long term damage to the Nintendo brand (and not nearly as bad as CD-i or 3DO), and the UMD was a very minor misstep as the PSP is still going strong