|all guitarists until proven otherwise|
What are you looking for in a guitar player? What strengths/capabilities do you feel are the most important? Any thoughts on common pitfalls?
Most of the following applies to any instrumentalist, not just guitarists. These are all situations I've been involved in, though I haven't had to hire people in all of them.
First, at some point in your career, “looking for” becomes a different process— you know a lot of guitar players, and people who know guitar players, so finding musicians is not a problem. It becomes more about “which of these people do I call for this thing?” It's a lot harder when you're just getting acquainted with a scene, are not confident about approaching the better players, and/or don't know any players at all.
Often who you get depends on things other than musical ability: Are they available? Will they do my thing for the amount it pays? Do I like them, and do they like me? Do they present themselves professionally? Are they ethical? Will they possibly hire me for their gigs if I hire them for mine?
It's also very dependent on what I want him or her for: membership in a band, a recording project, a casual, a regular gig, a tour, a road gig, a one-off creative project? Is it a normal jazz situation with a lot of playing, or is it a genre act/project— pop, swing, bossa nova, blues, country, etc. Is it a creative project where I need someone with a strong independent creative thing, that also works well together with mine? Is it a songwriter situation, where I'm helping get musicians for someone else's project?
General baseline musical competency things include: being able to perform with minimal rehearsals, or no rehearsals, being able to read, being a strong listener, knowing a lot of tunes, having strong rhythm, being into getting a professional sound, being a strong creative player. Typically players I do anything with have to have to be strong jazz players. A major thing I look for in guitarists is that they are strong rhythm section players— they know how to be a rhythm guitarist and accompanist, not just a soloist.
If I'm looking for someone for a paying gig playing tunes everybody knows, or reading normal charts, it's very easy: with whom do I like playing the most, and who is available for the date? And keep in mind: if you have paying work to offer, you can call anyone. Your assessment of your own playing, and of how much better they are than you, doesn't matter— everyone wants to hear from you when you're offering a paying engagement.
For a road gig (I'm really thinking cruise ship or hotel), it should be someone who can do the job, who I can also live with for weeks or months. Often it's younger players who are available for that kind of work, so they may not be extremely well rounded— they may have only a college-level jazz education (or equivalent) and that's it. For a tour (say, 1-3 weeks), it should be someone I like playing with, who will represent my music well, who will be easy to travel with. It could also be someone who will help get gigs, or whose name will help publicity, or who will help with tour logistics in some way.
For genre acts, the person has to know the style, including the major repertoire, and should be into getting the right sound for it. I usually only play with jazz guitarists, and some of them are only really able to do their own thing; others will have one or two other types of music in which they're interested, or have background, and are able to give an actual genre performance.
If I'm helping a songwriter or other solo artist find musicians, I'm looking for someone polished, well-rounded, with good pop sensibilities (or whatever genre is involved), who is service oriented, and is a quick study with new material.
For my own group playing my music, I want people who are easy for me to play with, who also have very strong musical personalities, and who like my playing and my project.
Pitfalls are the opposite of the above: they can't play (they play wrong stuff, they have bad time, they get lost, they can't acceptably fake styles they don't know, they are poor rhythm section players), they can't play the kind of music I need them to, they play too loud, they're hard to be around in some way, they don't like my project, they have substance problems, they act unethically or unprofessionally, or they aren't available when I need them. Most of these never come up— people with these kinds of problems never make it on my list of people to call in the first place. Including people who are always busy.
I'm afraid all of that may not be very helpful to the questioner— as I said, just trying to get names of people and figure out who you even want to work with can be a much harder situation. The only answer to that is to do a lot of projects, play with a lot of people, try to meet everyone doing paying work in your city, and hear them play. Then you'll begin to know who can do what, who you want to do anything with. At the same time, you will be developing yourself as a player who fulfills all of the above conditions, too.