You're right, loose and lose are two completely different words.

I suppose that could just be a typo too. But I doubt it. I think, in those cases, you're just seeing an example of poor grammar.

I'd call it poor spelling rather than poor grammar; it's usually misused in contexts where it's clear they were trying to use the verb "lose" and just put too many letters in it. Neither looseness, nor the "loosing" of, say, hunting dogs, is usually at all related to what they were trying to say. The root cause of the problem might be that "loose" and "lose" are pronounced differently only in the consonant sound, but are spelt differently only in the vowel sound.

Have the grammar skills of the general public really declined sharply over the last ten years, or has the advent of the internet just allowed us to see a more realistic cross section of the public?

I'd vote for the latter, with the additional effect that the Internet, and computers in general, have led to far more people producing prose as part of their daily routine than ever before.

Peter