my Querry is
if i build a software on a specific linux kernel [ older version ]
and then try to run it on another linux kernel [ new version ]
....what can be the possible problems
or what errors can most probably appear while running the binary in an updated version of linux.
Unless the program specifically uses some kernel facility which changed between the two versions, nothing much. More likely you will bump into problems with different library versions used by the program; again, those might ultimately depend on some particular kernel version, but typically, they don't. If the older version is very old (pre-2.6 or even pre-2.4) then some things like iptables have changed significantly, but those issues are the exception rather than the norm.
If you are using an rpm or deb package, it explicitly lists what versions of which libraries and other external dependencies it needs. It is rather unusual for these to depend on a particular kernel, but rather frequently, there is a dependency on a particular libc/glibc version.