Let's see....
One school never received my GRE scores from ETS despite me filling out the school code the day of the test. Coordinator was very helpful though and let me scan my copy to get my scores in. Eventually they let me know they got my actual official scores - in January, after I took the test in August.
I sent my transcript to another school in October but didn't submit my application until November. Because of this, they never matched up my materials and I didn't notice until the end of January that they still listed my transcript as missing!
A third school keeps sending me emails demanding a final transcript with degree shown before they will forward my application to the department. One problem: I'm a senior in college and don't HAVE a final transcript yet. No one in their admissions dept can quite figure this out, despite numerous phone calls.
The best one that's actually my fault, though, is waiting until 6:52 pm to submit my NSF GRF application for a 7pm deadline!