In Chinese, the tone can completely change the meaning, never mind the pronounciation. Examples:
妈妈骂马。Māma mà mǎ. (Mother scolds the horse).
Same basic pronounciation for each character, but different tone for each.
Or perhaps this mistake I heard once:
我很喜欢中国的人。wǒ hěn xǐhuan zhōng guó de rén. (I like Chinese people).
我恨喜欢中国的人。wǒ hèn xǐhuan zhōng guó de rén. (I hate people who like China).
As for spelling on the forums, I do appreciate when people take the time and effort to spell correctly. I find spelling errors really detract from what is being said. Plus, they may be very difficult for a non-native speaker to figure out. You can't look up a word if it's spelt wrong.
In the business world it would be very bad practice to not pay attention to spelling. It makes you look unprofessional, and people won't be as comfortable doing business with you. I have personally seen vendors dismissed from consideration for fairly large contracts simply because of a single spelling error. The same general feeling extends elsewhere. If you want to be taken seriously, you should take the effort to try and do things right. Also, constantly apologizing for the same thing looks bad. If there is a problem, people expect you to take corrective measures in fairly short order, not simply keep apologizing for the problem. If you recognize there is a problem, then you should do something about it.
Now granted, this isn't the business world, some people don't speak English natively, disabilities are a possibility, and typos happen. As such I think there should be some degree of tolerance. However, it's easier to tolerate a mistake when it's not happening repeatedly. If you've been corrected on a word, then try not to keep spelling it wrong in future posts. If something appears to be a typo I usually just ignore it (unless it's particularly funny). If it's just plain bad spelling, and the person doesn't know it, I guess I kind of like the idea of the mistake getting corrected. Gently. Everyone makes mistakes. If you're too hostile about correcting someone then they get defensive which will impede learning. I believe learning, and generally seeking to improve yourself to be a noble goal that everyone should strive for.
As for quick spell checks, I sometimes use google. If you're not sure about a word, do a google search, and see if it corrects you (and that the results are valid, and in the expected language). It's easy, quick, and requires no real forethought or effort installing things ahead of time. Or you could just use a paperback dictionary if you keep one handy by the computer. I actually frequently use a paperback dictionary to check my spelling before posting, and usually re-read most of what I've written to check for obvious grammar flaws.