There are two issues with the Login Menu item. These are reproducible in both 3.3.6 and 3.4.1 (clean installation).

First Issue

1. Create a Login Menu Item
2. Set the "Access Level" to "Guest"
3. Set the "Login Redirect" to "index.php"
4. Login on the front end and you will get the following error:

You are not authorised to view this resource.

Second Issue

1. Create a Login Menu Item
2. Set the "Access Level" to "Guest"
3. Set the "Login Redirect" to some other page, for example "index.php/component/tags/tag/2-joomla" (this is a valid URL with the default installation with English Sample Content).
4. Login on the front end and you will be forwarded to a wrong URL - the "login" word will always be added at the end of the URL, for example:

index.php/component/tags/tag/2-joomla/login

This was also reported in the forum.