Lastly, you need to definitely be sure that these people will write you a positive LOR. It would amaze you the people that actually do not write positive LORs for students. I was in a lecture recently and the speaker said that he used to be on an internship committee for a vet school, and some of the people that the applicants were asking to write them recommendations were actually advising against the applicant, and/or saying negative things about them. Seems like the writers would have notified the applicant prior to sabotaging their application, but that apparently was not the case. So, as susmtorm said, it is good to make sure that the people you choose know what you want them to write about and they are willing to stand behind that.
That's YOUR responsibility to ask for a good recommendation. If you ask someone to write a recommendation for you, they will write what they know. If they know more good things than bad, it would be unethical of them to give you a glowing recommendation. Anyways, you should never even be asking someone you think would remotely have anything bad to say about you. But even a good recommender will comment on your weaknesses in a non-damaging fashion, i.e. "while she is not the quickest worker, she is always very thorough" or something of that nature.
@OP
I'd still give my recommendation that the purpose of recommendation letters is to attest to your ability to succeed in:
1. veterinary school (ability to excel in sciences, research, etc)
2. professional school in general (work ethic, study habits)
3. as a veterinarian (evidenced by your behavior in experiences and the opinion of practicing vets.
Therefore, I think you should always have at MINIMUM 1 vet, who can attest to #3. #1 can be usually most succinctly and accurately described by a research advisor, professor, or academic advisor. #2 is the most general, and that's where you have some real wiggle room as far as who you get to give you the recommendation.
Basically, the end all and be all of the above novel is that I would worry less about the position of who you have writing the letter pertaining to #2, and more of how targeted/specific/focused they can be in their recommendation of you. Anyone can write a letter of recommendation, but it's up to you to find someone who can write you not only a glowing review, but one that stands out among the crowd of generic letters.