Giovanni, in a nutshell, is a cold, Sadistic, Cruel, pompous, Evil, calculating jackass.
Wait you need more than that?
Fine.

Giovanni is, in many ways, your typical criminal mastermind. He thinks nothing of treating his employees like dirt if they don't meet his high expectations (if he doesn't fire them outright). He wants to overpower all who oppose him, and, with that, he wants to rule the world.
So yeah, typical in many aspects.
Canonically, there is actually little more to him than that shown to viewers. He is shown as fairly petty, prideful, cruel to people and Pokemon alike, and is just shown as an overall jackass. Bring him a Pokemon he's never been shown before, and don't know what it does? Screw that, get it out of his sight.
He is implied to be a strong battler, as for a time he was the Viridian City Gym leader, but he doesn't care for his pokemon other than his Persian. He even tortures Mewtwo with the idea that he will conduct deadly experiments on Mewtwo's fellow clones if he doesn't submit to his will.
He takes an arrogant pride in his power and leadership abilities, and so far his only known motives are destruction and taking over the world. He seems to have inherited a good deal of it from his mother, Madame Boss, who was very similar (though it is to be noted she valued money moreso than power.).

Headcanonwise, socially he tries to at least put forth a smooth persona. This is the type of man who will have the women hanging on his arms, dazzling them with his money and good looks, as well as his charisma. He sees no trouble with sleeping around, as long as he's in charge and in power. Sex is power, after all. Other than this, he tries to keep a cool head, and would rather use veiled threats rather than get pissed off outright with people (the only time we see him in another setting other than straight Team Rocket, he uses such in public to get the point across to Jessie and James, rather than causing a scene.). Think giving the bellboy a death glare if they tripped and fell, spilling something of his. And manners are important. Can't have people you can use to your own ends thinking you're a rude fool.
In other words, what you see that seems to be a polite, smooth gentleman may just be your worst enemy.

The man has few redeemable factors, indeed.
In fact, the only canon example of him being anything but all oft his is that he treats his Persian quite well. And that is pretty much the only canon example.
Headcanonly, he has a son that, though. Though he and Silver have a bit of a distant relationship, (the kid left with his Nidoking for Johto B( ), he actually does love him. He just...doesn't really know how to show it.
And yeah, those are it.

Strengths:

• Physical
  • The guy is show in the anime to have a fair amount of muscle from what we see of him in The Evolution Solution, but how much is up to interpretation. Meowth seems to think he is more or less an Adonis in his daydreams.
  • Being a bigger guy muscle-wise, he seems to have a decent sense of balance, as Mewtwo Returns shows him being knocked around by explosions quite a bit.
• Mental
  
  • Giovanni is also figured to be a smart thinker when it comes to battles, or in turning things to his favor. We see this when he battles Gary in Battle of the Badge, where he misleads Gary into thinking he's winning by sending out Pokemon he believes will lose, all so he can show off Mewtwo's enormous power.
    
    • This, however, is often upset by heroes. B(
• Emotional
  
  • Despite his anger issues with his agents, he seems to be stable emotionally wise.
  • The guy seems to think himself amazing, and so there's no real lack of self-esteem. At all.
• Misc
  
  • His relationship with his son Silver is fairly good. Estranged -the kid took off with his Nidoking for Johto one day B(- and distant, but good.
  • Despite how cruel he can be, as I mention above, he actually cares a bit about his Persian. There is no "canon" reason given for this. POSSIBLE canon has that he rescued the cat as a child, but whether this is anime canon is up for interpretation. In either case, it's the only Pokemon he seems to treat with any degree of respect.
  • Charisma: he has plenty of it. How else do you command so many Rockets?

Weaknesses:

• Physical
  • We are not show any in canon.
• Mental
  
  • None shown in canon.
• Emotional
  
  • Did we mention he's evil? And sadistic and cruel and...
  • Pretty bad anger issues. He won't hit someone because of them, but there will be yelling and possible verbal abuse (calling his agents imbeciles and such is commonplace). The one exception to this is his son.
  • He rarely is anything but grumpy as well, at least from what we see up to Best Wishes (where we find he enjoys a cup of coffee in the morning like any good evil mastermind). See Anger Issues above.
  • Pride issues galore. This is everywhere in canon. A notable example is in Mewtwo Returns, where he is so caught up in the thrill of having Mewtwo under his control that he dismisses Domino's worries, thinking that he has won. (He's had this happen before to. :/)
• Misc
  
  • His relationship with his mother is...complicated. She was a harsh woman, and if he speaks of her -though he probably won't unless something amazing happens and he actually makes a close friend- it will more than likely be a mix of a genuine love for her...and lots and lots of mixed emotions. What little canon there is of it is found in the Birth of Mewtwo CD Drama.