I have fixed 5 bugs in /tests/ and added one feature to run-tests.php (a --runall option so testers can run the PHPUnit tests without using make - although make test still works). With these changes all of the tests in /tests/ now work. A unified diff patch is attached to bug ticket 20077.
I had to make an architectural decision when enhancing run-test.php with the --runall option. The bug ticked describes this decision and suggests two other ways to achieve the same objective. I chose the approach implemented by the patch because it required no changes to the directory structure of /tests/. However, I actually prefer the second possibility. So, if senior developers could look at the bug ticket description and give me some feedback (especially if they also think the second option is better), that would be great.
I also would appreciate some feedback on the following question. One of the tests referenced the global variables $wgDBadminname and $wgDBadminuser. When I ran the configuration script during Mediawiki installation on my machine, the LocalSettings.php file created defined the globals $wgDBname and $wgDBuser. So, I changed the test to use these variables rather than the 'admin' versions. However, I don't remember if the script gave me a choice to use the 'admin' versions or not. Also, if the configuration script has changed, then some installations may use the 'admin' versions and some may not. In either case, I would have to modify the bug fix to accept both types of global variable. If someone would fill me in, I can make any required changes to the bug fix.