To start out, I realize that I'm not that happy with the word in noun-form as applied to people. As several people noted, almost everyone does scummy things now and again. In general I'd rather categorize the deed than the person who did it.
A lot of scummy things aren't illegal. Not everything that's illegal is scummy. Some examples:
Just a few things which are illegal in certain areas, but which are not necessarily scummy:
- Drug possession
- Drug dealing
- Gun ownership
Some of that may have a significant correlation with doing things which are scummy (see the drug trade in Colombia, or Afghanistan), but I don't think they are inherently and necessarily bad things.
For contrast, things which are not illegal but which are scummy:
- Lying maliciously
- Spreading nasty rumors
- Custody battles over your kids to spite your spouse
- Walking out on your kids.
- Spiteful insults
- Taking credit for someone else's work
- Blaming another for your mistakes
Some of those are technically illegal -- bullying is a crime if it involves assault, harrassment can be crimal -- but in practice perpetrators are rarely arrested, much less convicted. In most cases, there's no benefit to prosecuting these as crimes: too hard to prove, too little obvious damage, whatever. But they're still scummy.
I said at the outset that I wanted to make a distinction between "doing scummy things" and "being scum", because pretty much everyone does unpleasant things now and again.
Still, if a woman told me that her ex-husband regularly broke promises to his kids, hardly ever got in touch with them, had lied to her boss in an effort to get her fired, often coerced her into having sex with him while they were married, tried to turn their friends against her, and deliberately paid child support late even though he had plenty of money -- and then she summed up with "He's scum", I wouldn't argue the point with her. Maybe he has reasons for all that, maybe in his mind it all makes sense and he's the injured party, but ... yeah. You can hate the sin and love the sinner, but it doesn't change the fact that he's a sinner, and probably unrepentant.
One of the facets to this, which I think does raise the number of scummy things going on in the world at large beyond what we tend to think of, is that many things that I consider completely unacceptable are normal, and even encouraged, in other parts of the world. Just because female genital mutilation is routine in a given country doesn't make it okay. It is, perhaps, harder to condemn the perpetrators of such acts when the bulk of their society is telling them "it's fine! Don't worry about it." Yet it's still wrong.