I think that anytime that you bring someone new into the testing field there are a couple of critical factors.
1) Tester Mindset - Do you have a mindset that I would attribute with a tester? Are you analytical? Do you have good problem solving skills? Are you able to learn and adapt to new technologies? How do you feel about repetitive work?
2) Chemistry - How do you feel to me? This is completely subjective and there is no tangible measure for it other than how do I feel you will fit in with our group. If you're not a good fit then I simply won't hire you. This could be based on any given number of factors, including anything that I think could be distruptive in the environment.
3) Communication - Where a good senior testing can be given an application and left alone for long periods of time, a new tester requries constant supervision and guidance, so if I can't understand you or you can't understand me and the points I'm trying to get across then it's a real tough sell. Verbal communication is HUGE in the training process.
4) Desire - Are you looking to do this as a career or is this just a job for you? We may not always want to be working on what we're working on, but we need to recognize that someone is depending on us. There are customers who will, ultimately, get this product and grade our performance. A lack of desire or interest in your work can cause catastrophic oversights that can lead to serious issues in a release.
I think these are all pretty important things, for any hire, but especially for a new hire because I think that you need to be exceptional in these areas to get into a position where they will be willing to train you. Remember, QA is almost always under-staffed, so if you make yourself a nuisance then you can sometimes be viewed as a liability.
9 out of 10 people I prove wrong agree that I'm right. The other person is my wife.