Continuing further down your OT pet peeve: how would you distinguish between people who know their English isn't perfect and are sorry about it (without saying so, per your advice) and those "morons" who are unapologetic about the same?
I have noticed that people tend to jump on others language skills in an indirect attack on the person when its the idea they disagree with. For some it is easier to dismiss an idea they do not agree with by attacking the person than refuting the argument.
Working with many foreigners I have run into the apology style more than once, they have good standing and do not wish to be dismissed for merely bad language skills. I live here and my use of the language is atrocious.
I've noticed three classes of bad English. The apologetic folk, who will often try to explain things in multiple ways, or be extra-verbose, in an effort to get their point across clearly. Second, the unapologetically bad folk, who write a semi-incoherent sentence and respond poorly to requests for clarification (often simply repeating the same sentence). Third, the lazy native (or fluent) speaker. This is an entirely new class of errors, which is easy enough to read through (being native and lazy myself), but sends a strong signal that I shouldn't place too much importance on what I'm reading.
Well, for those of us who fine at English, we can tell. The hard part is for you to determine if you yourself are correct.
It's more useful to invite constructive feedback than to apologize preemptively; that's what I'd recommend people do. Add onto this that, culturally, Americans tend to appreciate such invitations more than they appreciate apologies. (I can't speak to other cultures; I'm about 99% certain there are some major world-spanning ones where this is not true.)
I wish there was an easy and unobtrusive way to invite people to correct my English. Would it be okay to state that every once in a while in my comments? My opinion is that people don't like it, not because it's rude but because it carries the conversation off topic. I also wish there was a way to send a private message here to remedy that but maybe that's me over-complicating things.
If you're particularly worried about a specific post (for instance, you're uncertain of the right word when there are several words with similar pronunciations/spellings, or it's just longer than a normal post), I'd say just ask in that post. And regarding off-topic conversations, I say "meh". Most threads get derailed by far less productive side-discussions. I usually like to tuck corrections into actual conversation anyways. Respond normally, and then as an aside (may be first or at the end) comment on the correct spelling or usage of a word.
Certainly you could mention it as an offhand every so often, but the important thing IMHO is to make clear that you're looking to improve your English skills, as opposed to apologizing for whatever flaws you might have in your English.
The latter is usually needless, and can even imply that not knowing English well enough should be a source of shame, which is why it often draws calls saying not to apologize. It'd be like a 2m tall person apologizing for not being tall enough – you're already taller than most people, there's nothing to apologize for. ;)