Thanks for helping. You have a lot of points, so I'll address them in that order.

Perl 5.18.1 works just as well as 5.16.0. Which is to say that it has the same issues I mentioned earlier. The warnings are merely an annoyance.

I edited the actual names of the modules, scripts, etc because the names may have proprietary information. CG::CORE2 gave me no problems. I just shortened it to CORE for this post. I had no idea there was a module actually named CORE before posting here.

We have no logs, records, etc of what happened, or what we had before. 'r' does show a few modules that have not been upgraded, including DynaLoader. The full list is below. I have a new UPS, so a power outage is out. And no more mass updates for me!

Package namespace         installed    latest  in CPAN file
Alien::wxWidgets               0.62      0.64  MDOOTSON/Alien-wxWidget
+s-0.64.tar.gz
DBI                           1.628     1.630  TIMB/DBI-1.630.tar.gz
DateTime::TimeZone             1.62      1.63  DROLSKY/DateTime-TimeZo
+ne-1.63.tar.gz
Devel::Symdump                 2.10      2.11  ANDK/Devel-Symdump-2.11
+.tar.gz
ExtUtils::InstallPaths        0.009     0.010  LEONT/ExtUtils-InstallP
+aths-0.010.tar.gz
HTTP::Tiny                    0.036     0.037  DAGOLDEN/HTTP-Tiny-0.03
+7.tar.gz
Net::Ping                      2.38      2.41  SMPETERS/Net-Ping-2.41.
+tar.gz
Perl::OSType                  1.002     1.006  DAGOLDEN/Perl-OSType-1.
+006.tar.gz
Perl::Tidy                 20120714  20130922  SHANCOCK/Perl-Tidy-2013
+0922.tar.gz
Sub::Exporter::Progressive  0.001010  0.001011  FREW/Sub-Exporter-Prog
+ressive-0.001011.tar.gz
B                              1.34      1.42  RJBS/perl-5.18.0.tar.bz
+2
B::Concise                     0.89      0.95  RJBS/perl-5.18.1.tar.gz
DynaLoader                     1.14      1.15  NWCLARK/perl-5.8.6.tar.
+gz
Grid::Request::DRM::PBS       undef       0.9  VICTORF/Grid-Request-0.
+9.tar.gz
JSON::PP::Boolean             undef   2.27203  MAKAMAKA/JSON-PP-2.2720
+3.tar.gz
JSON::backportPP::Boolean     undef   2.27203  MAKAMAKA/JSON-2.61.tar.
+gz
657 installed modules have no parsable version number
(use 'o conf show_unparsable_versions 1' to show them)
[download]

I'm not sure about some of your non-exhaustive possibilities. Perl was installed before I even got here, so I'm not sure exactly how he did everything. The original installer may not remember either. But perl 5.16.0 did not overwrite the system perl. (We don't have root access at work. Even if we did, I hear that's just bad practice.) And my 5.18.1 was installed right next to his. In fact, right now, I'm installing a fresh copy of 5.16.0, just to see if it'll work as before.

Update! I just finished installing my fresh 5.16.0 install of perl, as well as a few CPAN modules. It still acts the same way as my updated 5.16.0, and 5.18.1. I am partially convinced that either something central to all installs went bork, or an up-to-date module is causing the problem.