Find someone that works in the company and become friends, or following. Then you can discuss the job, ask questions, etc. Example: So what made you interested in working for this company? How long have you been with the company? Do you enjoy working for this company, and let them know you are interested and what suggestions do THEY have in getting you in the door?

I think those are good networking vehicles to identify individuals involved in the hiring process for respective companies. I don't think just posting questions about your application will capture the right attention.

Hi Mike - Do you mean contacting the company through their Facebook or Twitter page to check on your application?