WP 3.8 Menu has lines??

Again, without touching anything on the site, can you check the admin area using another browser? And another computer?

I have a strong conviction that you have a plugin conflict, or that a plugin interfered with the update process when you ran your update, or that your update was somehow messed up. Your screenshots are not only displaying wrong, but they are also missing parts, which make me think that WP core was broken during the process. To fix this, or to get an idea about what the problem is, I think you should take some stronger steps. This is the process you should take:

The first of which is deactivating all of your plugins at the same time so that the only code running is your theme and WordPress core.

If the problem is still present with all the plugins deactivated, take the next step and switch to the default theme. This will load the site only with WordPress core (and its theme). If the problem is not present, test each plugin individually and then test the plugins in groups of 2-3 (since it may be a conflict between 2 plugins, not a plugin and WordPress). If you can locate a faulty plugin, deactivate it and contact the plugin developer with your findings.

If the problem is not traced to a plugin, and is still present when you have only WordPress Core (and a WordPress default theme active). Then do this: In the dashboard, go to Dashboard -> Updates. On that page, there is an option to Re-Install WordPress. Go ahead and click that button, but only do so while all the plugins are deactivated and you have a default theme activated.

If, after running the re-install, with no plugins active the problem still exists, come back here to let us know what you’ve done. If the problem doesn’t exist, then test the plugins by activating in groups of 2-3 and testing the dashboard with each group.

The process I’ve described is a basic troubleshooting process. The main thing is not to panic, this can be fixed, you just need to find the source of the problem. If all of these steps fail, it may help to manually re-install WordPress, but I can help you with that too and while it sounds scary, it is easy. Either way, I am confident that your issue is some kind of plugin conflict that will be resolved with the steps outlined above.

Let us know how it goes for you.

The other issue could be a local stylesheet or a browser extension interfering with the admin’s CSS.

This is via Safari on Mac OS 10.5

That OS was released in 2007 ! Is that the only place it has this issue?

@esmi – notice that on the dashboard, the RSS feeds are missing. That seems to indicate some customization, some plugin removing it, or Core is broken. A local stylesheet may be the issue more than a browser extension because it is occurring a different browser too.

notice that on the dashboard, the RSS feeds are missing

They could simply have been turned off via the Screen Options. I tend to turn them off myself.