The memory specs are pure cr@p.
512MBytes is not even sufficient to load the game, let alone to run it. When I start up a standard game (my system is XP/SP2) my memory usage goes up from 207 Mbytes to 576 Mbytes! You can see how much memory you have allocated by hitting Ctl-Alt-Del and checking the performance tab.
Naturally enough, memory usage continues to go up further as time goes on. This is perfectly normal since the number of objects that the game has to deal with also increases over time. This is completely aside from the question of whether the game has leaks. I have only played about half way through the game so far and memory usage is now close to 800 Mbytes.
For those who aren't aware, the OS is capable of allocating more memory than actually exists in the system. It manages this by copying information to and from the disk. Despite this, you should generally have more physical memory than allocated memory. The OS is capable using the rest for various purposes, notably a disk cache.
As soon as allocated memory exceeds system memory, you start to get in trouble. Since the OS is smart enough to swap out less used parts, this will start to manifest itself when you do something different than normal. In Civ4, this would be something like playing a wonder movie or accessing the Civilopedia. God forbid that you hit the Windows key because now it has to swap around entire programs.
As the amount of allocated memory gets larger and larger, things get worse and worse. At some point, the OS is not even capable of doing everything that you normally do without swapping stuff around. The system then slows to a crawl no matter what you do because it is spending all its time moving things back and forth between the memory and the disk. This effect is called "thrashing".
There are only two solutions: buy more memory

or stop playing the game.

This pisses me seriously because my laptop is only 4 months old. It was a package deal and I could only get it with 2 256MByte sticks of RAM. My computer doesn't thrash yet at 800Mbytes, but it's just a matter of time. Now I find that I immediately needs an upgrade. What's more, one of those sticks has to be thrown out.
Oh. Let me give a hint about memory leaks. If there is a leak in the game, you can "fix" it by saving, closing the game and re-loading. Be sure to close the program. At this point the OS frees all resources used, whether lost or not. To see whether there is a leak, look at the memory usage before saving the program and after re-starting it. If there is one, usage should go down significantly (a small decline is normal because objects are often allocated in a more efficient fashion when a program is re-started). If it doesn't, it means that the game is simply a memory hog and there is nothing to do other than to buy still more memory.