Teaching or giving advice without mentioning the Buddha Sometimes I see perfect situations to teach something from the Buddha and help someone with it, impermanence, worldly concerns, etc... however some people will immediately shut down and not listen if they know it was spoken by the Buddha... still I want to help.

So I try to focus on the teachings that can benefit them without saying in a explicit way it came from Buddhism (of course I do not say the teaching was mine as well, I just don't mention the source or say it is something I learned...)

Is that wrong, unethical or a cause for bad Karma? I have never thought about it!
There is nothing wrong with it at all. It is an extremely wonderful thing to speak the Dhamma in any form. In the Abhaya sutta (http://www.accesstoinsight.org/tipitaka/mn/mn.058.than.html) the Buddha said he used three factors to decide what and when to say something. They are truth, benefit, and agreeableness. The Buddha would only say something if it was true and beneficial to the listener, and if it was disagreeable, he would say it only at the right time and in the most gentle way possible. Because the Buddha is the perfect example of morality and right speech, we can use these principles to guide our speech as well.

When you say this you are saying something true, beneficial, and agreeable. Not only is there nothing wrong with it, but speaking the Dhamma is actually a kind of giving. In fact according to the Buddha:


  "The gift of Dhamma excels all other gifts." Dhammapada 354


Far from being a cause for bad Kamma, your action is actually a basis of great ammounts of good Kamma.