One thing to keep in mind as you read the forums is that people normally don't come to the forums and post unless they have a problem.  If you look at the number of people who have reported problems it is much smaller than the number who have success and don't encounter any issues with installation or upgrade.  People who encounter success generally don't take the time to report it, which is as it should be.  So, does this mean you won't have problems?  No.  But it also doen't mean that you will either.  The only way to know is to create a backup on a local machine and then try to perform the upgrade on the backup copy.  This is the only way to know for sure if your site will encounter any difficulty with the upgrade.

I don't have a reference right now, but keep looking here in the forums (or Google using site:www.dotnetnuke.com).  Someone posted a recommended procedure to upgrade from 3.x versions to 4.x using intermediate versions.  In other words, don't go directly from 3.1.1 to 4.5.1.  I know it looks like more work but it may go smoother this way.  Third party modules are almost always a problem also.

In any case, do test it in a copy of the site first.

Carlos