This may seem like a bold claim, but let's us examine a typical episode and we shall see how facts stand firmly by this assertion.
The rockstar coder
From this simple exchange we know that the Inspector is the hotshot rockstar developer. The Ninja! The Cowboy Coder! The man who has no concept of work-life balance! He drops whatever it is he is doing and goes off to solve the problem.
Once at work we quickly discover that he is more than a rockstar. He is, in fact, an incompetent fool who thinks he is the greatest thing ever. During the course of the entire show, Inspector Gadget does not manage to make a single thing better. All he does is run around from one place to another and try arbitrary things that are not in any way helpful or even rational. Examples include swinging a mallet around randomly (while breaking expensive pieces of arg), inflating his coat for no rhyme or reason (usually knocking innocent people over) or even helping the bad guys perpetrate their crimes because they just ask for his help.
At no point does anyone call Inspector Gadget out for clearly being a useless idiot who only does harm. The entire organisation would work more efficiently if he was kicked out. But yet he remains, having reached a high enough level on the police force's organisation chart that he can't be fired, or even challenged.
Here we find the only major disparity between Inspector Gadget the series and real life. In the latter, the incompetent rockstar (also known as Senior Systems Architect) breaks so many things that it takes more than one person to fix them. In extreme cases the group can consists of every other developer in the company. Perhaps this is the reason why Brain is portrayed as a dog. He does not represent a single person, but all of them.
If ew observe how Brain fixes the Inspector's bumblings, a common pattern arises. He always has to fix things in a way that the Inspector does not notice anything. Presumably if he were to notice these fixes, he would go back and change things back the way he left them. That is, completely broken.
Brain never does anything else, his life is a continuous stream of fighting fires that should never have been set alight. An illuminating example of this is the "pineapple incident" in episode Volcano Island, between 13m 54s and 14m 45s.
Penny is never given any credit for this. In fact whenever she tries to talk some sense to the other characters, she is actively dismissed and belittled. Once the case is solved everyone goes to Inspector Gadget and congratulates him for doing a good job. The Inspector replies with something like I solved the case? I guess I did. Like any incompetent rockstar he is willing to take all the praise without doing any of the work.
In light of this it should be obvious why the character of Penny is a woman.
The wild card
There are two differing theories on what he is supposed to represent. The first claims that he represents the company founder/owner who struck gold but since then has lost grasp of the present and just lashes out to his underlings at random.
The other theory claims that the creators of the show were incredibly foresighted and created Dr Claw as a prototype of modern day internet trolls 25 years before they actually appeared.