His English is probably a little better than my parents, who are also Asian, but I'm pretty sure he's just insecure since there are a lot of people who expect everyone to speak with perfect English. From what I've read, when Jackie first tried breaking into the US movie industry, he was told that audiences were put off by his lack of "good" English skills. There are some people who have a hard time understanding what people say when someone speaks with an accent, but that's not the fault of the person with the accent. I've always felt like Jackie Chan feels like it's something people can't overlook, but honestly, I think the majority of his fans who speak English don't care.

TBH I don't think his English is that bad. I think his English is easy enough to understand when he does interviews.

It's the same thing as when people complained that they couldn't understand Ken Wantanabe in "Inception". It wasn't as bad as people were claiming it to be.