Problems: if a homebrew application is put in the path in front of the default OS X version of the same, really anything might happen. Most common issues are caused by differences between the set of command line options available in the two versions, or differences in the meaning of the options. For curl the consequences might not be so bad, but for other applications you could, at worst, break the OS.
Keg-only: now you have two versions of curl! The default OS X, and the homebrew. If you want to use features that are not in the default but in the homebrew, you can do so by calling the homebrew curl explicitly. The precise path depends on how you've got homebrew set up. Because the newly installed version is not in the path, its unlikely to cause a problem unless it is explicitly called.