Have you noticed how many English people can't tell the difference between "there", "their" and "they're"?

I agree with you : we have exactly the same problem in French. I believe it comes from poor academic knowledge about grammar, and the meaning of the words. People write in the same way they pronounce words, but doing so they don't make the difference in the grammatical sense of the words. Should their sentences be written, then the words don't connect with their meaning if not spelt properly, hence the difficilty for the reader to understand a written message.