In the comics and Justice League Cartoon, Wonder Woman fights Mongul.  Can someone please explain to me why she hurts her hands when she punches him?  I mean she's hit Superman before and she doesn't hurt her hands so is is his face made of some material that hurts Amazons?

No, he's just far stronger than she is.  Mongul>Superman>Wonder Woman.
 
Her vulnerabilities aren't any different than Superman's.  Some might say she's vulnerable to piercing weapons like swords and arrows, but every time I've seen one do damage to her, the weapon was used by mythological figures or creatures, which means they were more than likely magic based, and WW has no special protection against magic.  In fact, those same kinds of weapons could be used on anyone from Superman to Batman, and unless they had some sort of magical invulnerability, they'd be cut and stabbed, too.

I remember that too. I went back and checked out he original story that episode was based on, Superman Annual 11 - For The Man Who Has Everything. I that comic Dianna hurt her hand punching Mongul as well.  So maybe they were trying to be
true to the original source material. The problem I see is while it is an established fact that Superman is stronger then Wonder Woman, the degree to which that is true seems to vary. This is only speculation on my part but since magic is one of the 
few thing that can damage Superman and Diana's powers are magic based it makes sense in a way that her punching Superman would be more effective that punching Mongul.

Correction guys. THE EPISODE WAS BASED ON THE PRE-CRISIS COMIC Superman Annual 11 - For The Man Who Has Everything. 
 In the PRE-CRISIS universe, Wonder Woman was MUCH WEAKER than she is now. That is the only reason she hurt her hand. If it was a post crisis comic, Mongul would have crashed against the wall since she is almost as strong as Superman.

Diana doesn't have any real vulnerabilities, every time one is introduced, it's retconned away or she gets over it (like how she's apparently immune to illusions and such).  
 
For this reason, she's generally shown to be weaker than Superman, Captain Marvel and the Martian, who all have a debilitating weakness (Kryptonite, reverting to Billy, and fire).   
 
The distinction was greater in the Justice League animated series. 

I don't read much wonder woman but is she bullet proof and if she is whats up with the bracelets

@BlackArmor: she is vulnerable to piercing weapons.

Don't bullets hurt her?

That episode was based off of the comic. And in that same comic, she punched him and hurt her hand while not really doing anything to Mongul because he was vastly superior physically.

I always considered Wonder woman to be the opposite of Superman in terms of vulnerabilities, while Superman has a high invulnerability to man made weapons, like bullets, bombs, etc, he is vulnerable to magic, while WW has a certain resistance to magic, but not to man made weapons (due to the Amazons not knowing much about man's world at the time she was created) so she can be hurt by bullets

@The Stegman said:

I always considered Wonder woman to be the opposite of Superman in terms of vulnerabilities, while Superman has a high invulnerability to man made weapons, like bullets, bombs, etc, he is vulnerable to magic, while WW has a certain resistance to magic, but not to man made weapons (due to the Amazons not knowing much about man's world at the time she was created) so she can be hurt by bullets

you are right about the bullets part but i have seen her tanking bombs and nukes..

@FadeToBlackBolt said:

Diana doesn't have any real vulnerabilities, every time one is introduced, it's retconned away or she gets over it (like how she's apparently immune to illusions and such). For this reason, she's generally shown to be weaker than Superman, Captain Marvel and the Martian, who all have a debilitating weakness (Kryptonite, reverting to Billy, and fire). The distinction was greater in the Justice League animated series.

This

I always considered Wonder woman to be the opposite of Superman in terms of vulnerabilities, while Superman has a high invulnerability to man made weapons, like bullets, bombs, etc, he is vulnerable to magic, while WW has a certain resistance to magic, but not to man made weapons (due to the Amazons not knowing much about man's world at the time she was created) so she can be hurt by bullets

Piercing objects are one of her weaknesses. Their have been versions where she is bulletproof, but for the most part she's been shown as vulnerable to piercing objects. Though they dont pose a great threat to her unless they are magically enhanced or a much more powerful form of piercing object, she can still be hurt by a bullet(but to her itd be like a bee sting or something pretty minute).

Also, she will not give up a fight. This is both a good thing and a weakness. She has great durability but she can die from over exhaustion if she fights for too long.

will have few weaknesses when batman had nothing to stop it... only the help of superman.

To your second point, I always thought that was a PIS kind of thing made up to give BM a "plan" to stop her ... it really doesn't fit the character of a great warrior, who would know when to pull a strategic retreat.

She has vulnerabilities to piercing weapons and, by Aphrodite's law, she will become as weak as any woman, if her bracelets are chained together. She's vulnerable to her magic lasso. She is vulnerable to psychic attacks, but having the magic lasso on her side seems to be the source of her resistance to psychic attacks and illusions; so, if Dr. Psycho wanted to attack her with his powers, he'll have to put one and two together and figure out that it must be done when she does not have her lasso near her. Diana was immune to psychic attacks, when/because she had Athena's eyes, but that is no longer the case. The thing is that most writers or the editors do not want to go back to these old weakness, so she has the appearance of invulnerability. These weaknesses were put there by her creator. To remove them would be a travesty to some, including me; also, I think Convergence restored her creator's desires, whereas, before, writers may a wiggled around it; unfortunately, Messner-Loebs of all writers may have remove or omitted the chaining the bracelets together weakness, but his run has often and is usually completely ignored; I'm not sure if he removed, however, because females tried to chain them, while Aphrodite's law required the tier to be male; Messner-Loebs didn't revisit the chaining the bracelets together properly with a male, so it was left unsolved, at best, or removed, at worse. I thought the Justice League episode with Mongul was precedent setting, but, in the New 52, at least, DC ignored that episode when she faced Mongul in the Superman/Wonder Woman book, but, now, we must ask, what are the after effects of Convergence?

My thoery is that Wonder Woman actually projects a psionic shield around her body. It's great for protecting her against blunt force attacks, and high levels of radiation, but is susceptible to more focused attacks.

true though ive seen it in other versions of Diana's character like in that JL movie where she fights the clones of Cheetah so i thought id include it

@willienotwilliam: JL Doomed ... Still PIS as she managed to lose about 99.99% of her brain cells

@muffin_sangria: I could buy into this for GA WW who had an array of psionic abilities or mental based gadgets.

@csg_cl: very true lol but since it was against cheetah i didn't mind as much

WW's primary enemies are (but not always) often trivialized when appearing against other heroes. WW herself is often displayed as under-powered by other writing teams. On top of that DC in general tends to be a bit more lenient than Marvel when it comes to checking power levels. And when you think about how bad Marvel tends to be at that..... yeah. Because of her place in DC WW is just destined to have tons of problems. She's the third favorite child, and not by much. She is iconic, and yet there is a darker side to her history (the whole bondage fetich weakness). She's always going to have a lot of oddities about her that don't make sense, but what we love about her isn't her powers, it's her personality.

Personally I've always wanted them to go back to this. Maybe not as diverse as her psychic abilities in the GA were, but at least training that includes some form of tactile telekinesis. We know for a fact that her powers didn't work that ay post-crisis, but as far as I know there is nothing contradicting her powers in the New 52 having some sort of psionic training factored it.

LOL fair enough :)

I agree ... I've always thought the training as the source of her powers was the best origin :)

Personally, I just want WW to be more... idk, "godly". She's the god of war, she needs to extra powers beyond commanding soldiers

Superman and other popular characters are her main weakness.

well, she's gotten a few other abilities as well ... she seems to be immune to major telepathic attacks as of Doomed when Brainiac could not take her mind over (and she repelled Lois-Brainiac's attack as well). She was immune to the Amazo virus too, which affected the rest of the league so that's a little something.

Mental vuln: May lose control of her temper, or humanity.

Physical vuln: Is not completely impenetrable like Superman. And is vulnerable to gas attacks...ie.chloroform, mustard gas, etc. But does not destroy her as easily as regular humans, due to Fountain of Youth and Amazonian physiology.

At least that's the original concept by WMM.

That show's non canon, but it was based on a comic where she did hurt her hands in said comic. Anyways, sharp objects of course hurt her. So she has them bracelets to block them.

xoxo, -Saint Sophie