I want to update my glibc from 1.2.10 to 2.12. Are there any problems regarding dependency for other tools and software currently installed using previous version of glibc on CentOS release 6.3 (Final) with kernel 2.6.32-279.9.1.el6.x86_64?
Absolutely. The rest of the system must be upgraded along with it. Otherwise a whole lot of binaries will cease to run because they are linked against a different version of Glibc.
In cases where the upgrade is minor, this tends not to be an issue.
If you name your distro an version, people might give you more specific answers.