A lot of video games use the same libraries to make different things work, and increase "code reuse" at the same time (less stuff to re-invent or rewrite). I've made it a habit of the last few years to maintain a copy of the latest DLLs to use with different games as they're needed. This won't always work, but its certainly worth trying if a game is running slow or glitchy.
In my current cache of DLLs, I have the following...
Comb through your Program Files / Program Files (x86) directories and find the latest versions, then copy those to folders with older versions. Feel free to rename the old ones first for safety.
Another thing is that a lot of games and programs use parts of different Microsoft runtimes and libraries. If you're running Vista or 7, you most likely have newer versions in the System32 or SYSWOW64 folders of your WINDOWS directory. However, you don't need to make copies of these: just move the old ones somewhere other than the program's directory, and it should use the new ones. Pretty much anything labeled "msvc" is replaceable: if its missing, you're usually told, and you can put the other file back.
If you just had the idea of putting the newer non-Microsoft DLLs in the System folders, don't: it usually doesn't work.