<p>Are there any limitations on the amount of memory that the Flash player can use? If you have a SWF that over time gets a lot of data from the server, then more and more data will be kept in memory. Is there a limitation on this?</p>

Not in any version of Flash that runs on desktop PCs. As long as your application keeps using more memory, desktop Flash will keep requesting it from the OS, until the OS runs out of memory or something crashes. Of course you the developer should limit your memory usage as appropriate, but Flash won't force you to do so.
In Flash Lite (the mobile version designed for cell phones), the host application imposes preconfigured limits on memory usage, but that's probably not what you care about. :)