Adverbs. It's not that people use them incorrectly, it's just that they don't seem to use them at all.
"Man, he's running fast!"
Man, he's running quickly
"Why is this car in front of me going so slow!?"
Why is this car in front of me going so slowly?!"
It also bugs me when people use prepositions when they're not applicable.
"Where are you at?"
The 'at' is not necessary. It's redundant.
The improper conjugation of verbs annoys me to no end as well. I'm sure you've all heard plenty of people saying "we be" and "I is".
The thing I've had the most trouble explaining to people is the english subjunctive. For example, a person would be trying to put himself in a situation and totally fail grammatically at doing so:
"If I was an astronaut, I'd be on the moon by now."
No! No! No!
If I were an astronaut, I'd be on the moon by now.
That's it for my ranting for now.
