If I log out of one account while vBSSO is enabled and log into another, it gets stuck at the "Thank you for logging in" screen. Some sort of redirection loop. What can I do to fix this?

Could you please contact support team http://vbsso.com/report-an-issue/ describing the steps you use to reproduce your case on your website.

Thank you,

Keep up to date with the latest news on http://vbsso.com/

Great modification no doubt.

But I wonder if there are any real impacts to server performance from log library files?

We have found no issues in log4php and server performance during the term we work with this lib.

It's wide-spread library for logging and it is used in many projects.
If you want - you can use simple logging: just to comment lines 17-20 and 22-24 in
\vbsso\includes\functions_logging.php

Merry Christmas and Happy New Year!

Does the plugin works with wordpress 4.1?

Plugin has not been fully tested but it seems to be working properly. All the available information is accessible at http://vbsso.com/.

We are happy to answer any questions and discuss any concerns you may have. Please do not hesitate to contact us.

Does the plugin works with vbulletin 5.1?

Any vBulletin 4 plugin will have to be remade from scratch for vBulletin 5 (and sometimes that's not even possible), so no.