I am running a website on a local machine to test out the steps invlved in upgrading the current version of our web site to a stable release of version 5.

the upgrade path I am using is:
4.9.5 to 5.0.1 to 5.1.4 to 5.2.3 to 5.3.1.

As soon as I upgrade to 5.0.1, the web site gets numerous javascrip errors which stops you from completing the majoirity of the tasks on the website.

On loading the portal there are 2 error messages:
  Invalid argument
  'this.rootNode' is null or not an object
 

when you press the login link (or register) there is an error:
  'dnn.controls.submitComp' is null or not an object

when you select the minimize button there are 2 errors:
  'undefined' is null or not an object
  'dnn.controls.submitComp' is null or not an object

Is there anything special that I need to do when I upgrade or is this only a problem with local machines?

I tried to upgrade straight to 5.3.1 but the same error occured.

 That did it for me, previous guy probably doesn't want to admit it ;). After all these years of development, didn't think the cache would get me.