Peter:
Essentially, the long gun registry is a database set up to track all firearms classed as 'non-restricted' in Canada. A non-restricted firearm's basic legal definition is one which is not restricted or prohibited; you can find the RCMP's interpretation of the regulations at List of Restricted and Prohibited Firearms.
All non-restricted firearms have been required to be registered since 2003, although there has been an amnesty in place to the present date.
The basic complaints with it are:
1. It's ineffective. Estimates are that less than 40% of the non-restricted firearms in Canada are registered.
2. It's costly. So far, about $2.5billion has been spent on the program. It was sold to the public as costing at most $2million. That would be a 1000X cost overrun.
3. It's insecure. A report came out a few years showing that the database has had many unauthorized accesses over the years, and there are rumors that copies are floating around.
4. It's inaccurate. People routinely find firearms registered to them that they have never heard of, or sold and transferred away years previous. Note that these people would be criminally liable to produce these firearms if demanded by police.
5. It doesn't apply to criminals. Since they don't register their firearms anyways. In fact, it only applies to firearms owners who are the statistically safest and most law abiding demographic in Canadian society.
6. It's useless for police anyways. After all, with all the above, if the registry says there are no guns in a house, do you believe it? Or if the registry says there are 6 guns in the house, can you trust all 6 are there, and no more? Or that all 6 entries are legitimate and correct? One officer (Daniel Tessier) already died because he believed the registry when it said there were no guns in a house.
That's just skimming the surface of the issues surrounding the long gun registry. The biggest injustice is that it's pushed forward by the left wing anti-gun establishment as fixing a variety of ills from women's rights, to suicide prevention, to lowering crime rates, despite there being absolutely no scientific / statistical evidence to prove that it's had a measurable effect on any of these statistics.
Our current conservative government has committed to scrapping the long gun registry, and has a bill to do so in progress, hopefully to be passed this spring. In the meantime, the beaurocracy (RCMP and Canadian Firearms Program) is working hard to reclassify as many non-restricted firearms as possible to restricted and prohibited status while they still have a convenient list of owners. And these owners of reclassified firearms are getting notices that they must turn in their firearms for destruction if they do not have the appropriate license class.
That's the really short version that covers some of the major issues; for more details, you can join the Canadian Gun Nutz forum, and quickly hear more about the issue than you would ever care to know!