Application developed in C may use dynamic libraries (.so files) to reuse the
common functions/symbols in the binary. If the library is missing, application
will not run. Some of the libraries were removed between CentOS 6 and CentOS 7.
From your CentOS 6 packages, following libraries disappeared:

_codecs_iso2022.so from python-libs
db2.so.0 from krb5-libs (required by NonCentOS signed package(s):libgssglue )
ha_archive.so.0 from mysql-server
ha_blackhole.so.0 from mysql-server
ha_example.so.0 from mysql-server
ha_federated.so.0 from mysql-server
ha_innodb_plugin.so.0 from mysql-server
libI810XvMC.so.1 from xorg-x11-drv-intel (required by NonCentOS signed package(s):xorg-x11-drivers )
libQtAssistantClient.so.4 from qt-x11
libabrt_web.so.0 from libreport
libakonadiprivate.so.1 from akonadi
libbrasero-burn.so.0 from brasero-libs
libbrasero-media.so.0 from brasero-libs
libbrasero-utils.so.0 from brasero-libs
libcamel-provider-1.2.so.19 from evolution-data-server
libck-connector.so.0 from ConsoleKit-libs
libcupsdriver.so.1 from cups-libs
libdrm_nouveau2.so.2 from libdrm
libedataserverui-1.2.so.11 from evolution-data-server
libegroupwise-1.2.so.13 from evolution-data-server
libevdocument.so.1 from evince-libs
libevview.so.1 from evince-libs
libgdmsimplegreeter.so.1 from gdm-libs
libgdu-gtk.so.0 from gnome-disk-utility-ui-libs
libgdu.so.0 from gnome-disk-utility-libs
libgnome-desktop-2.so.11 from gnome-desktop (required by NonCentOS signed package(s):gnome-screensaver )
libgnome-window-settings.so.1 from control-center (required by NonCentOS signed package(s):orca )
libgnutls-extra.so.26 from gnutls
libgvfscommon-dnssd.so.0 from gvfs
libhal-storage.so.1 from hal-libs
libhal.so.1 from hal-libs
libipq.so.0 from iptables
libkipiplugins.so.1 from kipi-plugins-libs
libldif-2.4.so.2 from openldap (required by NonCentOS signed package(s):python-ldap )
libmp.so.3 from gmp (required by NonCentOS signed package(s):mpfr )
libmysqlclient_r.so.16 from mysql-libs
libnepomukqueryclient.so.4 from kdebase-workspace-libs
libnih-dbus.so.1 from libnih
libnih.so.1 from libnih
libnss_winbind.so.2 from samba-winbind-clients
libnss_wins.so.2 from samba-winbind-clients
libpackagekit-glib.so.12 from PackageKit-glib
libpanel-applet-2.so.0 from gnome-panel-libs
libpangox-1.0.so.0 from pango
libparted-2.1.so.0 from parted
libpolkit-backend-1.so.0 from polkit (required by NonCentOS signed package(s):python-slip-dbus rtkit DeviceKit-power )
libpolkit-gtk-1.so.0 from polkit-gnome
libpython2.6.so.1.0 from python-libs
librpcsecgss.so.3 from nfs-utils-lib
libsnmp.so.20 from net-snmp-libs
libstdc++-libc6.2-2.so.3 from libstdc++
libtime_solar.so.4 from kdebase-workspace-libs
libverto-k5ev.so.0 from krb5-libs (required by NonCentOS signed package(s):libgssglue )
libvte.so.9 from vte
libwebkit-1.0.so.2 from webkitgtk
libxcb-atom.so.1 from xcb-util
libxcb-aux.so.0 from xcb-util
libxcb-event.so.1 from xcb-util
libxcb-property.so.1 from xcb-util
libxcb-reply.so.1 from xcb-util

We checked the requirements in Non-CentOS signed packages, but for the non
rpm-packaged binaries, you should check the compatibility list yourself
by using e.g. ldd <binary> command.
If some of your application uses the library on the list above, you may need
to get the .so library from different place or search for an alternative.