How to apply patches in MySQL in any version
The concept of "applying patches" is not meaningful in MySQL unless you are building from source, and even then, it's not really a question that has an answer, since they don't release "patches."

What are you trying to accomplish?  What version are you running, now?  When you say "applying patches in MySQL 5.1.67," do you mean applying fixes found in 5.1.67 to a server of a previous version?  

I ask that, because, at the time of this writing, 5.1.67 is still a very recent release and I would contend that "so many bugs" is not a phrase that describes this release at all.  It (5.1.67) is very stable and is, in fact, my current production release of choice for everything based on 5.1.  

The fixes present in 5.1.67 cumulative from the beginning of 5.1.  To have these fixes, you have to have 5.1.67 because changes made to 5.1.67 would often depend on other changes made to intermediate versions.  Hence, you upgrade.

Within a release series (e.g., 5.1.x) the functionality of the server should not change after the series reaches General Availability, and the release notes will document any incompatible changes that are introduced.

Upgrading should not be a problem within a release series (although you should always have backups, of course).  It also should not be a problem going from series to series either, as long as you follow the instructions and don't try to skip over a major release series.