One way to understand what it takes to land the right job is to look at the problem from the other guy's perspective: that of the IT manager with an open slot.
One significant aspect of this is organizational - others are things like relative age, maturity, courage, leadership vs management, strategic IT direction vs applicant skills, etc.
In government and psuedo government organizations the power of the HR department is virtually absolute in the short term and susceptible to change only over a term of years and many, many, job postings. What happens there is simple: it's possible to beat HR in the short term, but in the longer run they always get the last harrah. As a result HR rules generally prevail at the minion level - meaning that a CIO who doesn't expect to last long anyway may be able to hire someone knowledgeable as an assistant, but the manager for accounts processing has to follow "open competition" rules and choose from among the people HR decides to pass along.
Objectively this would be one of several good arguments for disbanding HR as a corporate cost and productivity sink, but in the reality of organizational compromise HR exists as a control on nepotism and other hiring abuses - because ownerless organizations like governments and big public companies lack anyone willing to fire managers sticking to inappropriate hiring and compensation decisions.
As a result experienced IT managers in these kinds of organizations tend to delegate most of the real decision making to HR simply because it's easier to over-staff with look-alike middle-of-the-pack people than to continually fight both HR and the internal auditors to hire and protect exceptional ones.
As a corolary, the key to getting hired by this type of organization is to look the part: meet HR's expectations for what a Role X employee looks like, and you'll get the job this time or next. And all that stuff they tell you about looking for a go getter? a broad range of skills? a self starter willing to take on additional responsibilities? It's just smoke - walk into HR and prove to them that you understand the organization's business and are prepared to make a significant contribution to its IT component -and what you'll get is a sincere promise to keep your resume on file.
On the other hand, the guy who needs to hire someone in an organizational context where he actually has control and is motivated the find the best possible applicant, faces a wholly different set of decision criteria - because he really is looking for someone to take off some day to day presure and help make things work.
Those differences in organizational behaviour aren't driven from a single factor, but the most important one comes from a related organizational issue: employee role management within the organization chart.
Most organizations with strong HR departments also have large, traditional, data processing groups. In those, job roles tend to be closely defined - and the people part of IT management often consists more of enforcing job boundaries than it does of any kind of positive effort to build careers or reward ability. Thus when your local government, University administration, or financial services company announces a job posting for a "database support analyst" they're usually also saying that any skills you may have beyond whatever they define a database support analyst's job as, will not just be wasted: they'll be actively penalized with any attempt to expand or use them strongly discouraged.
Organizationally that's terribly wasteful: the organization is paying for the employee's full skill set, not the 5% applicable to the slot he's budgetted into - so in leadership organizations where the focus is on IT contributions to the business, your new boss is going to want to see the opposite of what HR does: a wide range of skills and a willingness both to teach what you know to others and to learn more stuff as you earn greater responsibilities.
In this situation the ideal condidate is one who extends the team, is ready to take on new challenges and doesn't flinch at standing up for his ideas - pretty much the opposite of what HR is looking for.
So what's the bottom line if you're job hunting? understand the other guy's expectations and meet them or, more succinctly: when in Rome, look like a Roman.