Here's what I've gathered from posting on here, and from clinicians:
GPA and rank of course play a part in your application, but just a part. People in the medical field understand that you may not be strong at lecture exams, and why that can be a reason for a low GPA/rank. Of course you want the best grades possible, but it is ONLY just a part of your application. However, you need to have excellent LORs that demonstrate how you are as a person, and future clinician. Programs want to know if you can critically think through a case, and are able to display excellent communication and empathy towards clients. One thing that I have heard from some clinicians that I really never knew about was if you are one that pours a cup of tea and loves gossip and drama, or one that steers clear of it. Most of the academic residency programs require a MS or PhD to be completed in which previous research work looks VERY good on your application. Of course a publication will make you look golden, but it is not necessary. Most private practice residencies don't require a publication, but some do. From what I know, internships look at LORs as a determinant of whether they want you or not. I met a clinician from one of the biggest hospitals in the USA, and she said that she reads LORs first, and then the rest of your application so she can know who she is going to admit or deny. I have not heard much about VCA/BluePearl sponsored residencies, and will look out for what they are in this thread!