Unable to update packages using yum, too many missing requires

I'm trying to update all the packages on my system, and it's preventing me because many packages has missing requires of lib****.so.##()(64bit).

See the output after accepting yum update --skip-broken below:

ERROR with transaction check vs depsolve:
php-common(x86-64) = 5.3.3-40.el6_6 is needed by (installed) php-imap-5.3.3-40.el6_6.x86_64
httpd-mmn = 20051115 is needed by (installed) mod_perl-2.0.4-11.el6_5.x86_64
httpd-mmn = 20051115 is needed by (installed) mod_python-3.3.1-14.el6.1.x86_64
** Found 38 pre-existing rpmdb problem(s), 'yum check' output follows:
libaps-1.0.7-798670.14062518.x86_64 has missing requires of libarchive.so.2()(64bit)
libaps-1.0.7-798670.14062518.x86_64 has missing requires of libicuuc.so.42()(64bit)
mod_perl-2.0.4-11.el6_5.x86_64 has missing requires of httpd-mmn = ('0', '20051115', None)
mod_perl-2.0.4-11.el6_5.x86_64 has missing requires of perl(:MODULE_COMPAT_5.10.1)
mod_python-3.3.1-14.el6.1.x86_64 has missing requires of httpd-mmn = ('0', '20051115', None)
mod_python-3.3.1-14.el6.1.x86_64 has missing requires of libpython2.6.so.1.0()(64bit)
mod_python-3.3.1-14.el6.1.x86_64 has missing requires of python(abi) = ('0', '2.6', None)
openldap-2.4.39-8.el6.x86_64 has missing requires of libsasl2.so.2()(64bit)
openscap-1.0.8-1.0.1.el6.centos.1.x86_64 has missing requires of libpcre.so.0()(64bit)
openscap-1.0.8-1.0.1.el6.centos.1.x86_64 has missing requires of librpm.so.1()(64bit)
openscap-1.0.8-1.0.1.el6.centos.1.x86_64 has missing requires of librpmio.so.1()(64bit)
perl-BSD-Resource-1.29.03-3.el6.x86_64 has missing requires of perl(:MODULE_COMPAT_5.10.1)
php-imap-5.3.3-40.el6_6.x86_64 has missing requires of php-common(x86-64) = ('0', '5.3.3', '40.el6_6')
plesk-core-12.0.18-cos6.build1200140606.15.x86_64 has missing requires of mysql-server >= ('0', '5.0.60', None)
plesk-core-12.0.18-cos6.build1200140606.15.x86_64 has missing requires of vixie-cron
plesk-core-12.0.18-cos6.build1200140606.15.x86_64 has missing requires of db4-utils
plesk-rdbmspp-2.0-735641.14062518.x86_64 has missing requires of libicui18n.so.42()(64bit)
plesk-rdbmspp-2.0-735641.14062518.x86_64 has missing requires of libicuuc.so.42()(64bit)
plesk-service-node-utilities-12.0.18-cos6.build1200140606.15.x86_64 has missing requires of librpm.so.1()(64bit)
plesk-service-node-utilities-12.0.18-cos6.build1200140606.15.x86_64 has missing requires of librpmio.so.1()(64bit)
pp12.0.18-bootstrapper-12.0.18-cos6.build1200150126.15.x86_64 has missing requires of mysql-server >= ('0', '5.0.60', None)
psa-autoinstaller-3.16.20-140624.15.x86_64 has missing requires of librpm.so.1()(64bit)
psa-autoinstaller-3.16.20-140624.15.x86_64 has missing requires of librpmio.so.1()(64bit)
psa-libxml-proxy-2.7.8-14033112.x86_64 has missing requires of libboost_program_options.so.5()(64bit)
psa-mail-driver-common-12.0.18-cos6.build1200140606.15.x86_64 has missing requires of libpcre.so.0()(64bit)
python-iwlib-0.1-1.2.el6.x86_64 has missing requires of libpython2.6.so.1.0()(64bit)
python-iwlib-0.1-1.2.el6.x86_64 has missing requires of python(abi) = ('0', '2.6', None)
sw-cp-server-2.0.5-201405151701.centos6.x86_64 has missing requires of libpcre.so.0()(64bit)
sw-engine-2.13.12-centos6.201502091549.x86_64 has missing requires of libicudata.so.42()(64bit)
sw-engine-2.13.12-centos6.201502091549.x86_64 has missing requires of libicui18n.so.42()(64bit)
sw-engine-2.13.12-centos6.201502091549.x86_64 has missing requires of libicuio.so.42()(64bit)
sw-engine-2.13.12-centos6.201502091549.x86_64 has missing requires of libicuuc.so.42()(64bit)
sw-engine-2.13.12-centos6.201502091549.x86_64 has missing requires of libxmlrpc_cpp.so.4()(64bit)
sw-libboost-regex1.54.0-1.54.0-14020622.x86_64 has missing requires of libicudata.so.42()(64bit)
sw-libboost-regex1.54.0-1.54.0-14020622.x86_64 has missing requires of libicui18n.so.42()(64bit)
sw-libboost-regex1.54.0-1.54.0-14020622.x86_64 has missing requires of libicuuc.so.42()(64bit)
sw-libpoco-1.4.3p1-14062518.x86_64 has missing requires of libpcre.so.0()(64bit)
sw-nginx-1.6.0-1.14051516.centos6.x86_64 has missing requires of libpcre.so.0()(64bit)
Your transaction was saved, rerun it with:
 yum load-transaction /tmp/yum_save_tx.2015-02-16.23-19.XxK6ji.yumtx