Registration updates don't stick and when updating another users profile from the Directory module I get:

An error has occurred.
Error: Dynamic User Directory is currently unavailable.

Anyone else having any issues with the modules on 4.5.1?

I have not seen this.  Is there any more information in the Log Viewer of DNN you can post.  Without seeing that, it could be an error in a RegEx validation.

I upgraded to Dynamic Registration 2.4 on a DNN 4.0.3 site and it worked great. I upgrade to DNN 4.5.1 and now I get Method not found: 'Int32 DotNetNuke.Security.Authentication.UserController.AddDNNUser(DotNetNuke.Security.Authentication.UserInfo)'. 

John,

We are still in the process of testing 4.5.1. As a practice we have always upgraded DNN from the previous version. In the past I have seen some dlls in the bin folder not get upgraded. I would check the versions of the DNN dlls in that directory. As long as you backed up your 4.0.3 you can roll back to that version, and do incremental upgrades of the DNN core. I know that the guys at DataSprings have tested on DNN 4.5. Also as a practice, I like to wait at least 30 - 45 days of major DNN releases to start testing. If I see this occur in our lab I will repost with what I find.

Also check your upgrade log for DNN.