Mathematics in modelling: Issues? Are there some known examples where the use of mathematics in Economics (as opposed to economic intuition or experience) has led to flawed models or some other kind of issues?

I often hear people say that they don't like the use of mathematics in economics .... but why? So I was wondering maybe it lead to flawed models, perhaps because human behavior isn't as nice as some mathematical equation?
Math is a tool. You can hardly blame a saw when you fail to sharpen your knife with it.

So is math necessarily a poor tool? In my view, it's a wonderful language through which concepts can be expressed concisely and unambiguously. It's quite powerful to express an economic problem as a math problem because oftwn this means the problem is already solved in full generality (e.g. Recognizing an incapacitated lot problem as an integer programming problem which has easy algorithms for solution).

I've heard some complaints that the temptation to pretend a problem is accurately modeled by a solved math problem is quite strong - this is probably one of the issues you're getting at. Again, nothing wrong with using a tool its proper place. The fault is unambiguously with the user.