Decrease Bugerror based on Design Pattern?

The whole approach, or a way of thinking, is wrong. The design patterns have nothing to do with amount of bugs.

Those patterns are published to help developers avoid repeating some design work again and again, using well-tuned design solutions developed by other people before. You may understand it better if you read this article: http://en.wikipedia.org/wiki/Design_pattern[^].
Design pattern in not theory, it's a generalized design solution which have its limits of applicability and certain rationale. One cannot "have" the pattern. A developer can use the pattern only after she/he analyzed possible approached to the solution of some problem and can judge if one or another pattern can be useful. Some developers try to see the use of a patter as a goal of development; and this is a big mistake — the goals are set by the prospective use of the programming system, its utility, and some pattern can be nothing more that one of the many means for reaching these goals. In some pathological cases, developers try to stick all patterns they know in some project. The is like adding problems for the sake of solving them.

Now, as the the bugs, the whole situation is well described by one proverb from my native culture:
"For a "good" dancer, even his legs make a hassle". (Actually, more popular folk version of this proverb uses more explicit language, mentioning some other bogy parts. :-)) A patten can help to reduce the number of bugs only indirectly, in cases when it helps to write less code, for example. A person who tends to make many bugs due to lack of accuracy and regular approach, poor understanding of technology and best development practices will add even more bugs in the implementation of the design pattern. :-)

—SA