Most of the times I saw design patterns being applied, they were applied as a way to find a solution, so you end up twisting a solution -- and, sometimes, the problem it self -- to fit the pattern.
My guess is that the heavy use of "let's apply this design pattern" before even understanding the problem -- or even trying to solve it -- comes as a form of cargo cult: "We saw that people used this pattern and solved their problem, so let's use it too and it will solve our problem". Or, worse: "Design pattern is described by Famous Person, so we must use it".
Here is the thing: Design pattern should not be used as a way to find solution to any problems. You may use some of them as base for your solution, but you must focus on the problem, not the pattern.
"Do a visitor pattern will solve this?" is the wrong question. "What should we do to solve our problem?" is the real question. Once you went there and solved the problem you may look back and see if it is a visitor pattern -- or whatever pattern. If it doesn't, that's alright, 'cause you solved the problem. If it did... well, congratulations, you now know how to name your solution.
I've seen this happening a lot: People have a problem; people decided to use a pattern; the pattern doesn't actually solve the problem (not in the 100% mark, but above 50%); what happens then is that people start twisting the problem to fit the pattern or, worse, add new layers to transform the problem into the pattern.