Right now, crossing one of the magical rep borders happens more or less unnoticed. People just gain the particular powers. Now, of course they have eagerly been awaiting this moment, and want to start using their new powers instantly.
However, this leads to people---usually with good intentions---doing stuff that is actually discouraged. The most notable case is users who passed the 500 boundary starting to tag questions as "not-programming-related", "belongs-on-serverfault", or the like.
They do this because they can't close yet, but want to do what they can to get the question noticed for 3k-rep users to close. They're most likely not clear that this is unwanted behavior. I'm not claiming I haven't fallen into this myself when I passed 500.
Another example is closing. I often see question being voted to close for an obviously unfitting reason. I assume that this is often done by recent 3k-gainers, who are just happy to have found a question that they might use their closing powers upon, but are just a little too eager.
I propose a pop-up (like the "You've earned a new badge" one) saying something like "You have earned the power to retag questions. Please read our retagging guidelines [link] for a short introduction".
This probably holds for the 500 (retagging), 2000 (editing), 3000 (closing) and 10.000 (deleting / mod) boundaries.