Auditioning isn't much fun, whether you are the one under fire or the one making decisions. If you are the one looking for people to form a band, think about what it is you want them to do.
An example, if you want someone who can read music, then you are going to want to have some charts ready to test their reading skills. Can they ready fluently, slowly or not at all? This can be just one of the ways you choose the most suitable addition for your band.
Are musical styles important?
Be sure to go through the entire range of musical styles you expect the person to be able to play. Group jam sessions won't cut it, everyone plays every blues lick they know, as fast and as loud as they possibly can. Get to know the musician you are auditioning. Do they play other styles like reggae, or R&B, do they play multiple instruments, or any instrument that may add some spice to your sound? Many Musicians have been through some sort of music program, whether it be a high school band where they learned String or Brass instruments, this may be the sound that makes a particular song sit just right with you.
If you are auditioning for a band..
Look from the bands perspective, Be honest about your strengths and weaknesses. Don't pretend to be a jazz player if you don't know what a C6 Chord is. Get to know the band you are auditioning for, try and figure out what it is that you can add to the band that would convince them to hire you. Have you written any songs? Can you write arrangements? Do you own recording equipment? Do you have band equipment? Could the band rehearse in your garage? Most importantly, is this a band you want to be in? Just because you are offered a job does not mean you have to take it. Don't waste your time or others doing something that you do not want to do.