This question is similar to Provide a mechanism for users to comment on a job listing in its goal but (1) aims at different phases of job search (2) solves the manpower issue raised in the answer.
I recently applied to one of the jobs on Careers, got the confirmation email from SO and then never heard from the company. However, there is no way I can learn if I shot for the wrong company or they never respond to uninteresting CVs or they are slow to respond and so on.
It would be helpful if Careers displayed some basic info about companies.
It could display whether all submitted applications get at least a response (if so what is the average response time). This could be efficiently done either by asking the company if they do so when they put up the ad (an extra check-box) or allowing applicants to mark their progress in the application. This would require no manual work since the applicant could forward the acknowledgement email from the company back to Careers.
It would also be useful if hiring rate for companies was shown. I am not familiar with the mechanics of Careers to suggest an efficient way of gathering such information.