The error message when I run yum update reads:
Transaction Check Error:
file /usr/lib/libmad.so.0.2.1 from install of libmad-0.15.1b-13.fc12.i586 conflicts with file from package libmad0-0.15.1b-4.fc16.i686

I've looked at other file conflict threads, and they ask for the results of yum repolist all, so I posted that below.

Loaded plugins: langpacks, presto, refresh-packagekit
repo id repo name status
atrpms Fedora 16 - i386 - ATrpms enabled: 797
atrpms-bleeding Fedora 16 - i386 - ATrpms bleeding disabled
atrpms-bleeding-debuginfo Fedora 16 - i386 - ATrpms bleeding - Deb disabled
atrpms-bleeding-source Fedora 16 - i386 - ATrpms bleeding - Sou disabled
atrpms-debuginfo Fedora 16 - i386 - ATrpms - Debug disabled
atrpms-source Fedora 16 - i386 - ATrpms - Source disabled
atrpms-testing Fedora 16 - i386 - ATrpms testing disabled
atrpms-testing-debuginfo Fedora 16 - i386 - ATrpms testing - Debu disabled
atrpms-testing-source Fedora 16 - i386 - ATrpms testing - Sour disabled
fedora Fedora 16 - i386 enabled: 20,176
fedora-debuginfo Fedora 16 - i386 - Debug disabled
fedora-source Fedora 16 - Source disabled
livna rpm.livna.org for 16 - i386 enabled: 5
livna-debuginfo rpm.livna.org for 16 - i386 - Debug disabled
livna-source rpm.livna.org for 16 - i386 - Source disabled
rpmfusion-free RPM Fusion for Fedora 16 - Free enabled: 355
rpmfusion-free-debuginfo RPM Fusion for Fedora 16 - Free - Debug disabled
rpmfusion-free-rawhide RPM Fusion for Fedora Rawhide - Free disabled
rpmfusion-free-rawhide-debuginfo RPM Fusion for Fedora Rawhide - Free - D disabled
rpmfusion-free-rawhide-source RPM Fusion for Fedora Rawhide - Free - S disabled
rpmfusion-free-source RPM Fusion for Fedora 16 - Free - Source disabled
rpmfusion-free-updates RPM Fusion for Fedora 16 - Free - Update enabled: 688
rpmfusion-free-updates-debuginfo RPM Fusion for Fedora 16 - Free - Update disabled
rpmfusion-free-updates-source RPM Fusion for Fedora 16 - Free - Update disabled
rpmfusion-free-updates-testing RPM Fusion for Fedora 16 - Free - Test U disabled
rpmfusion-free-updates-testing-debuginfo RPM Fusion for Fedora 16 - Free - Test U disabled
rpmfusion-free-updates-testing-source RPM Fusion for Fedora 16 - Free - Test U disabled
rpmfusion-nonfree RPM Fusion for Fedora 16 - Nonfree enabled: 150
rpmfusion-nonfree-debuginfo RPM Fusion for Fedora 16 - Nonfree - Deb disabled
rpmfusion-nonfree-rawhide RPM Fusion for Fedora Rawhide - Nonfree disabled
rpmfusion-nonfree-rawhide-debuginfo RPM Fusion for Fedora Rawhide - Nonfree disabled
rpmfusion-nonfree-rawhide-source RPM Fusion for Fedora Rawhide - Nonfree disabled
rpmfusion-nonfree-source RPM Fusion for Fedora 16 - Nonfree - Sou disabled
rpmfusion-nonfree-updates RPM Fusion for Fedora 16 - Nonfree - Upd enabled: 310
rpmfusion-nonfree-updates-debuginfo RPM Fusion for Fedora 16 - Nonfree - Upd disabled
rpmfusion-nonfree-updates-source RPM Fusion for Fedora 16 - Nonfree - Upd disabled
rpmfusion-nonfree-updates-testing RPM Fusion for Fedora 16 - Nonfree - Tes disabled
rpmfusion-nonfree-updates-testing-debuginfo RPM Fusion for Fedora 16 - Nonfree - Tes disabled
rpmfusion-nonfree-updates-testing-source RPM Fusion for Fedora 16 - Nonfree - Tes disabled
updates Fedora 16 - i386 - Updates enabled: 6,398
updates-debuginfo Fedora 16 - i386 - Updates - Debug disabled
updates-source Fedora 16 - Updates Source disabled
updates-testing Fedora 16 - i386 - Test Updates disabled
updates-testing-debuginfo Fedora 16 - i386 - Test Updates Debug disabled
updates-testing-source Fedora 16 - Test Updates Source disabled
vortexbox Packages for VortexBox enabled: 49
vortexboxbeta Packages for VortexBox disabled
repolist: 28,928

(FYI, vortexbox is from http://vortexbox.org, which is the source of my original installation, and is based on Fedora 16.)

---------- Post added at 04:43 PM ---------- Previous post was at 03:24 PM ----------

I deleted the repository rpmfusion-free.repo from /etc/yum.repos.d and was able to successfully run updates, so the rest of my system is up to date at least.

rpmfusion-free.repo showed up back in the directory after restarting, so I don't know that this is a permanent fix, or if I'll have to manually remove that file every time I want to update my system.