offending

what happens if you have offended a Japanese person?
For example if you didn't use your chopsticks the right way or blowing your nose in front of them

It entirely depends on the person. Many will pretend that nothing has happened, i.e. you won't notice anything. Others will try to teach you the proper way. A few might be shocked with an open mouth. Etc.

They probably won't tell you unless you were very close friends. And if you're not Japanese they'll probably shrug it off, so there's probably no need to mention it; just don't do it again.

Don't be too worried about blowing your nose. Japanese people recognise that this is necessary sometimes! If you have to then turn aside, do it as quietly as possible and then say "Sumimasen"- that is much better than sniffing loudly, whatever you may have heard.

Also Japanese people will be highly impressed if you can even hold the chopsticks properly, so not much need to worry there either. Foreigners in Japan get a lot of leeway- you are unlikely to offend anyone as long as you are polite, and don't wear your shoes inside!

"what happens if you have offended a Japanese person?"

This has been answered by other posters.

"For example if you didn't use your chopsticks the right way or blowing your nose in front of them"

They'll take it for granted.

what happens if you have offended a Japanese person?
For example if you didn't use your chopsticks the right way or blowing your nose in front of them.

Pretty much they'll ignore it. Depending if it's a friend or a stranger though. Stranger might stare... but if you're a stereotypical-looking gaijin they'll stare at you anyways. As for the chopstick thing... it'll get annoying but, every Japanese person you meet will compliment you on your awesome ability to use them. This goes if you can speak even the slightest bit of Japanese too. Oh and if you're cute looking you'll hear "kawaii" everyday. Going back to insulting behaviors though, if it's a friend they might let you know.

For example, on msn, i used "heehehee" as a laugh in katakana with a friend. She told me my laugh was scary because it sounded like a perverted middle aged man's laugh. To me, it's just a giggle... but... she let me know and I told her how it is in America and also how our korean friend laughs the same way. She responded, "Yea... she does laugh weird, huh?"