For those of you who have been on the receiving end of cover letters, resumes, and word samples for summer internships...

How would you say firms handle the process most of the time?

I've mostly heard firms allow applications to come in, then around April they begin responding (it seems most summer internships are listed as beginning in late May).  

Would you say this is the popular approach among firms or is it split between responding fairly quickly (say within 2 weeks) and the method described above?

Just for kicks, are there things (mistakes) that will get your application put right into the trash?

I appreciate the insight!