Trello seems like a perfect fit for this, for me at least. Just have different lists for different application statuses. Record special notes or links as commen

Trello seems like a perfect fit for this, for me at least. Just have different lists for different application statuses. Record special notes or links as comments on individual cards. I'm curious what more you have in mind that this approach wouldn't handle well. I guess the main thing that would be missing is direct integration of emails sent to and from the various companies.