In light of the recent problems at Walter Reed, I was very interested in hearing what the GAO had to say about the VA. In a report titled Veterans' Disability Benefits: Processing of Claims Continues to Present Challenges, the GAO tells us that the VA has actually improved its procedures over the years, but that filing claims and appeals is still an arduous, overlong process, and that the VA's disability policies are probably out of step with the modern world.
As the following chart shows, the VA actually reduced its pending claim backlog in the early 2000s.

However, following a commendable low in 2003 -- the year of the Iraq invasion -- the backlog started to pile up again. By the end of last year, initial compensation claims took an average of 127 days to be processed, up 16 days from the year before, and appeals resolution took an average of 657 days.
Consider that this means that our veterans are currently waiting just over four months to have claims processed, and potentially another two years if they try to appeal a rejected claim. That's a long time to hang out, disabled, waiting for help.
The VA notes that they're receiving quite a few more claims than they used to, due to our pair of wars and other causes:
The increase in VA’s inventory of pending claims, and their average time pending is due in part to an increase in claims receipts. Rating-related claims, including those filed by veterans of the Iraq and Afghanistan conflicts, increased steadily from about 579,000 in fiscal year 2000 to about 806,000 in fiscal year 2006, an increase of about 39 percent. While VA projects relatively flat claim receipts in fiscal years 2007 and 2008, it cautions that ongoing hostilities in Iraq and Afghanistan, and the Global War on Terrorism in general, may increase the workload beyond current levels. VA also attributes increased claims to its efforts to increase outreach to veterans and servicemembers. For example, VA reports that in fiscal year 2006, it provided benefits briefings to about 393,000 separating servicemembers, up from about 210,000 in fiscal year 2003, leading to the filing of more original compensation claims. VA has also noted that claims have increased in part because older veterans are filing disability claims for the first time.
Newer claims also take longer to process because they involve harder-to-substantiate conditions, all neurological -- post-traumatic stress disorder (PTSD) and brain injuries (the latter a notable consequence of near hits by IEDs). In processing PTSD the VA runs into specific roadblocks based on the need to substantiate the causative incident(s):
Additionally, claims-processing timeliness can be hampered if VA cannot obtain the evidence it needs in a timely manner. For example, to obtain information needed to fully develop some post-traumatic stress disorder claims, VBA must obtain records from the U.S. Army and Joint Services Records Research Center (JSRRC), whose average response time to VBA regional office requests is about 1 year. This can significantly increase the time it takes to decide a claim.
The VA, aware that its improving outlook has taken a retrograde turn since the invasion of Iraq, has a number of plans to fix the situation. Their fiscal year 2008 staffing request is a 6% increase over 2006 levels. They intend to bring the additional staff up to speed quickly using overtime from regular staff and training led by retired VA employees. They also want to capture more of a servicemember's military records electronically at discharge, so they can cut down on problems such as that one-year wait time from JSRRC. They're also trying to cut down on problems that lead to appeals.
The GAO applauds these efforts, but points out that the VA may have an antiquated idea of just how disability works these days:
Specifically, our research showed that the disability programs administered by VA and the Social Security Administration (SSA) lagged behind the scientific advances and economic and social changes that have redefined the relationship between impairments and work. For example, advances in medicine and technology have reduced the severity of some medical conditions and have allowed individuals to live with greater independence and function in work settings. Moreover, the nature of work has changed in recent decades as the national economy has moved away from manufacturing-based jobs to service- and knowledge-based employment. Yet VA’s and SSA’s disability programs remain mired in concepts from the past, particularly the concept that impairment equates to an inability to work.
If I'm reading that correctly, GAO is pushing in a good direction here. The ability to work in some capacity should not, alone, be a metric that a veteran is no longer in need of assistance and care. We want our injured veterans to return to a real life, not just to survive.