I just updated to 3.7.1. From the Dashboard when I click the "Visit Site" on the admin bar at the top of the screen some of the links now appear as dark blue until I hover over them when they are light gray. The only link that displays correctly is the +New one.

As I remember it, the last time I updated WordPress I had the same problem and finally had to edit a CSS file, I think. After several hours of poking around I still can't figure out what to do to fix this problem and, of course, no longer have my notes from last time.

After I posted the above request, I looked at earlier posts that I had made and saw that when I had the problem before, it was suggested that I switch to Twenty Twelve to see if I had the same problem. I went back and switched to the Twenty Twelve theme. When I did the admin bar looks fine and I can see all the links. I switched to ATA and had the problem. I switched to my child theme and had the same problem. So it looks like it is theme related?

You updated Atahualpa to 3.7.1? the current release is 3.7.12.

what version of WP are you using?

I click the "Visit Site" on the admin bar at the top of the screen

You mean the WordPress toolbar bar? that has nothing to do with the theme, WP puts it there.

I'd suggest using FireBug in FireFox so you can see the CSS being applied.

I'm using WordPress 3.7.1 and ATA 3.7.12. Am curious why the problem goes away when I switch to Twenty Twelve and comes back when I activate ATA again.

This is because of the way CSS works

CSS rules are applied based on the precedence of the selector (the part before the {…})
The rules of a more specific selector override

In this case, the CSS being applied to the link by the WP admin CSS are not specific enough to override one of the selectors in the Atahualpa CSS.

You could edit the WP CSS and add

#wpadminbar .quicklinks > ul > li > a, #wpadminbar .quicklinks > ul > li > .ab-empty-item {
    border-right: 1px solid #333333;
}

to

#wpadminbar .quicklinks > ul > li > a, #wpadminbar .quicklinks > ul > li > .ab-empty-item {
    border-right: 1px solid #333333;
    color: #00FFFF;
}

changing the #00FFFF to the color you want or you could put it in the CSS Inserts option.

Frankly, before you pointed this out, I never noticed this and I doubt it will ever bother me.
If it really bothers you, you should open a issue with wordpress to have them fix it permanently.

I added the code to my custom CSS and it works fine. Will report the issue to WordPress. Thanks for your help.