The reported issues with installation of Silverlight Tools has been relatively low. But, there have been a handful of issues reported on the Silverlight.net forums, mostly involving Service Pack 1 for Visual Studio 2008 (which is required before installing Silverlight Tools). Some users have had trouble with the installation of SP1. For those people, I highly recommend hitting up the brilliant folks on the MSDN forum. They are far more experienced in the bigger Visual Studio installation experience.
The most common problem directly related to Silverlight Tools, though, is users who have encountered the message "Build 9.0.30729.XX of Visual Studio 2008 SP1 or Visual Web Developer 2008 SP1 must be installed before installation can continue."
First off, why does the build number matter? Part of the Silverlight Tools installation includes a patch for Visual Studio required to add functionality such as the XAML designer. This patch is specific to a build of the product - it works with SP1, not SP1 Beta, not RTM. Attempting to install this patch on the wrong build will either 1) best case - not provide the functionality you were looking for or 2) worst case - mess up your installation of VS causing problems later down the line.
But, when some users look at their build information, it says they ARE running build 9.0.30729. The quick answer is that most likely the SP1 installation was only partially successful and you need to uninstall and re-install SP1. The more detailed and helpful answer is that you should read Jimmy Lewis's blog on Silverlight Tools Speed Bumps which has all sorts of helpful information, suggestions, and workarounds. Thanks, Jimmy!