Do You Mind If I Go Blogging This?
My second thought, while I appreciate the language analysis of such sentence and its relatives, is that the ability to construct proper sentences is not the same part of the brain that speaks. Oh, they do cooperate, but writers and speakers are not the same ilk. Writers benefit from self-editing (writing, then re-reading what was just inscribed) and editors (who aren't watching for content as much as mechanics) to make sure their sentences are accurate within the Rules of American Language. When you're speaking, it's a cascade of proper words quickly grabbed off the shelf and placed in as close a proper order as possible; people often aren't sure how they're going to end the sentence when they start it, hence the mixups of tense and action. If it works, and people understand it, then that assembly of words gets put back on the shelf, intact, for quick retrieval later. This is part of why people say "um" instead of pausing, and use the word 'like' as an all-purpose word and punctuation. It works, so the unconsious word-assembler keeps using it. Writing and proper english requires consious assembly, which takes longer than speaking. It's almost suspicious when people speak too properly or correctly; it's assumed they're reading off a script, like those so-called "real customer testimonies" on the toothpaste commercials. Nobody uses words and contractions like that. Real sentences are full of misplaced contractions, invalid suffixes and prefixes, ums, and restarted sentences.
So, I generally forgive improper language (although I annoyed the girls more than once for picking on the whole "can I" or "may I" thing) when spoken -- otherwise, you'd spend your entire life annoyed. Remember people's words are coming out of their head faster than their internal editor can keep up, and start feeling a little sorry for real-time subtitlers.