Take this first part with a grain of salt, because it is perhaps influenced by my having worked as a contractor for so many years.
Consider looking at a contractor if your ability to pay is such that you can't attract top talent in a full-time capacity. If you're paying too little and asking for too much you're going to either get poorly skilled employees, employees who have glaring defects that may not be skill-related (poor interpersonal skills, substance abuse issues, etc), or you'll end up with a "revolving door" position where employees work for awhile and leave for better pay.
If your company is hung-up on both paying too little and needing someone for a given period of time, as opposed to fulfill a given set of tasks, then you're probably in a hopeless scenario. Likewise, if the tasks will keep a full-time employee busy and the company is planning on paying too little, then it's also hopeless. You will get what you pay for in the long run, one way or another.
My guess is that you don't really have a full-time need, and the company could probably spend the planned salary, or less, on a contractor who would do everything you need.
A contractor is much easier to "get rid of" if the relationship is a "bad fit". A contractor can typically be much more flexible than a full-time employee re: work logistics (weekends, evenings, etc). A good contractor is going to treat your company's needs with a very high degree of skill and care because they know how easily your company can sever the relationship and look elsewhere.
This is going to sound really trite, but more than any of the other items below, pay attention to your sysadmin's ability to communicate with others. Basic writing and speaking skills are important, and do a lot to indicate the state of the mental processes occurring "behind the scenes". A sysadmin's work should involve communication with other IT and non-IT employees, and an ability to communicate effectively is essential. Having an ability to form analogies and communicate abstract concepts is certainly nice "icing on the cake", but if your sysadmin can't even write complete sentences or speak complete thoughts then it's hopeless already.
There are points in everybody else's answers that ring true to me re: a "bad fit" (be it an employee or a contractor). I've been the guy who helps companies bridge the gap between firing a bad sysadmin and hiring a replacement, and I've seen a number of bad scenarios play out. (Being the person who is changing passwords, looking for "back doors", etc, while the sysadmin is over in the CEO's office being fired is fun work, but stressful, too.)
Some "IT specific" nasty attitudes I've seen (cribbing from some parts of other posters' answers here, unashamedly) in dysfunctional situations include:
Rip everything out and start over: It's one thing to identify something that's a "ticking time bomb" and take care of it, but often in IT I run into (often immature and entry-level) sysadmins who seek to "build an empire" in their image, and obsess over removing old infrastructure for the sake of installing new. It's one thing to make a business case supported by facts and ROI projections, but I've seen this particular dysfunction as being nothing more than a strong personal drive to replace systems for the sake of replacement.
I can't tell you that: These are the sysadmins who, while taking a strong personal ownership stake in their work, go too far and become overly possessive, secretive, and paranoid. The computers belong to the business, not the sysadmin. Failure to document work, disclose passwords, or be open about how systems work (or fail) isn't a good sign. I've heard some sysadmins cite "security" as a reason to be secretive, but security by obscurity isn't security. I've also heard sysadmins with this attitude say things like "Yeah, but if I give the passwords to so-and-so they'll just screw it up." Usually, this is accompanied by a veiled or overt statement of fear for being blamed if something goes wrong subsequent to the disclosure. If a business is so unstable that this fear is justified the sysadmin would do better to leave and find another job than to play games with secrecy.
Blame somebody / everybody / anybody else: These are the sysadmins that constantly cite third parties, their predecessor, or the users experiencing issues as the cause of problems. Certainly, there are issues caused by all these factors, but a pattern of consistent and repeated finger-pointing is a bad sign. We've all had to deal with hardware errata, software bugs, and users creating problems for themselves. Being able to identify one of these sources as a root cause to an issue doesn't make it finger-pointing. Being unwilling to investigate an issue and identify a root cause, though, combined with the reaction of vaguely waving hands and saying "It's gotta be that buggy Windows / Linux / Cisco router / etc..." is cause for concern.
Power trip: These are the sysadmins who delight and setting up roadblocks for users because of a personal agenda or a perceived business agenda. Again, it's one thing to place limitations on users for justifiable business reasons. It's quite another, though, to be the "preventer of IT services" simply for the mad power rush of being able to control others. I've seen this particular dysfunction extend into really nasty things like "e-stalking" of employees by reading their email, covertly performing screen / session captures, listening to phone calls, and just generally being a "creepy" person to others.
Policies don't apply to me: Often combined with the "power trip" attitude, these are the sysadmins who refuse to be subject to the IT policies that they, themselves, otherwise enforce or dictate. While it can be benign and harmless, I've seen this cause nasty situations like threatened sexual harassment litigation (a sysadmin surfing and prominently displaying work-inappropriate content). Sysadmins are in trusted positions, and need to maintain an attitude of professionalism. Part of that attitude means playing by the same rules and being accountable like everyone else. Just because we have the ability to perform activities "off the record" w/ our elevated access permissions and rights doesn't mean that we should do it.
Can't admit weakness: It takes a strong person to say "I don't know the answer to that, but I can find it for you." Everyone has gaps in their knowledge and experience. This particular dysfunction often results in situations where a sysadmin ends up vastly over their head. It's important to take calculated risks in career development, and it can be said that great personal growth occurs when people "bite off more than they can chew" and succeed. On the other hand, great expense (or outright failure) for a business could easily occur when a sysadmin decides to tackle important issues like disaster recovery or IT security and fails for lack of ability. Managers who unreasonably disallow their employees access to third-party resources / training / support can help to create this kind of culture. No one should be penalized for admitting that they don't know how to do something while expressing a willingness to help find the right answer (or, even better, learning how to do it themselves).
These are my toys: This is the sysadmin who treats the business IT infrastructure as an exciting toy. It's one thing to identify a particularly interesting technology that happens to fulfill a business need well, but it's quite another to influence a business to spend money on technology for the unstated purpose of being something fun to play with. I've seen situations where sysadmins became enamored with a given technology and decides to bring that technology in to solve a problem not because it's suited to the business need, but because it's something they'd like to play with. I've seen this happen all kinds of things: fiber optics, virtualization, SAN gear, wireless networking, etc. Management should keep this in check as much as possible, but non-technical managers may always understand if a given technology really is something the business needs or not.
I've always done it this way: This is the sysadmin who is dead set in their ways. Usually, I've found this combined with an attitude of "I don't want to learn about new things", too. Our field is changing. Some of the work that we did 10 years ago is automated today, and some of it remains the "same old, same old". Everything about our industry is constantly being revised, updated, and refreshed. Best practices change more slowly, but even they change too. It's unreasonable to expect that every sysadmin will keep up with the "cutting edge" of technology, but it's also unacceptable for a sysadmin to languish in years-old technology showing no sign of interest in updating skills. If a business is a growing concern, its IT operation should be forward-looking. (Obviously, there's a balance here, too. You can tip the scales too far and end up in a "these are my toys" scenario, as well...)
No understanding of business: Business "does IT" because it helps in doing business efficiently. Any other use of IT in business is counter-productive. Too often I've seen sysadmins who are unaware of basic concepts of accounting and business (revenue less expenses equals profit, etc). I would never expect a sysadmin to be an expert in accounting, but I would expect them to understand the basic way in which a business incurs expenses for the purpose of turning a profit. In poor economic times, especially, it's nice to have your sysadmin understand where the money comes from and why the business makes the decisions it does related to where the money goes. A sysadmin who believes that IT stands apart from the "business" part of the business isn't an asset.
No desire for continuity: In today's occupational culture, it's should be assumed that we'll all work for a variety of employers. Our job today isn't, statistically, going to be our job forever. A good sysadmin should prepare documentation not because "they might get hit by a bus", but because their eventual replacement will need it. An unwillingness to prepare documentation because of perceived "job security" reeks, to me, of an individual who has no desire for upward mobility. I don't work for a single employer anymore, but if I did I'd be planning for what I was going to be doing next, and keeping documentation up to date so that my replacement will have better time of it (just like I'd like from my predecessor at my next job).
