This has nothing to do with the upgrade, but would only be setup related. This was a sticky post in the Joomla 2.5 category of the forum, but I'm pasting the reply here and will also make this post sticky for the Joomla 3.x category... as it still comes up occasionally.
If you have an event that is set as Public, but it still is saying that you must be logged in to register... the solution is the same every time. It's a setup problem... not a bug. Guaranteed.
First, if your login message is the default Joomla login message, this would be because your DT Register menu item is set as Registered or Special. This will affect all of your events as they'll use that ItemID and require a login to access those links.
Second, if your login message is the private event message coming from DT Register...
There are two features that will force events to require login. Both are explained in the tooltips for these features, and also explained further in our video tutorials:
1) Overlapping Event Check - if you enable this in the main configuration area of DT Reg, ALL of your events will require login.
2) Prerequisite Events or Categories - in each event, you can select prerequisite events and/or categories. If you do, the event will then require login. If you accidentally selected something here not knowing what it was, you can de-select using CTRL-Click (or Command-Click on a Mac).
The two parameters in configuration about prerequisites have nothing to do with this. They do not enable/disable the prerequisite feature... they only modify how it is applied.
One of these two HAS to be the reason. I promise. If you read this and say "no, I don't have these checked. It's something else." Sorry, but you would be totally incorrect. No offense.

There is absolutely no other reason a public event would require a login.
Also, note that the category access level of the event has nothing to do with this. For a public event, the category should of course be "Public" (NOT "Guest"), but if the category isn't public, then the user would not ever SEE the event... thus not have the opportunity to try and access a registration form. The Public/Private setting within the event doesn't affect who sees it, but who can proceed to the form. Thanks!