First, Objective Morality. The argument usually goes something like this: In order for morals to be derived objectively, there has to be some kind of authority stating that something is either moral or immoral. One action cannot be more moral than another based solely on one’s opinion that something is good or bad. Therefore, based on the subjective nature of atheistic morality, the “Golden Rule” is no more moral than Hitler’s genocide because it is simply a matter of opinion.
So, I propose a new argument. Logically, one cannot base an objective statement on a subjective experience. Experiencing god through a spiritual experience (i.e., a burning in the bosom, seeing a vision, or hearing a voice) is a subjective experience. Therefore, you cannot say that the morals you get from a god are objective without first demonstrating objectively how you know god exists and is the source of your morality. Once you can demonstrate the objective existance of god, then you can claim an objective source for morals, but not before. Because of this, I find the argument for objective morality to be null.
The “God of the Gaps” argument goes like this: if science does not have a good explanation of an event or process, then god must be responsible for it. In other words, you can freely stick god in to any gaps in our scientific understanding. This is very common among young earth creationists (who actually take it one step further and deny evidence or explanations so they can cling to their god explanations), and most level-headed people see this as a bad argument right away. But many people, including myself a few years ago, fall in to this line of thinking without realizing the fallacy (see what I did there?).
The logical fallacy here is called an “argument from ignorance.” This basically means that just because you don’t know how something works or how something came to be, you can’t just insert a belief as an explanation (“if not X: then Y” is not a supported argument, it is merely an assertion). Going back to the creationists, even if we found out that evolution was completely wrong, creationists would still need to provide support and evidence to say that creationism is true.
So what happens when we do find scientific reasons for things where people have inserted god? This is the problem with the “god of the gaps” argument. In this scenario, God is “ever receding” in to gaps of scientific ignorance, until one day, he can’t hide any longer and must be discarded. This is why Galileo was exiled by the catholic church for using physics to show that the earth revolves around the sun and not the other way around (as indicated by the bible, and thus the pope's objection). If this is your basis for belief in god, prepare for this eventuality.
**With regards to the “Thou shalt not kill” commandment (which, by the way, is a mistranslation and should be read “Thou shalt not murder your fellow Jews”), there is actually a rather convincing secular or evolutionary reason, as well as a psychological reason, to not kill one another. The evolutionary reason is pretty straightforward. Populations which are predisposed to not killing each other, will propagate better and be more successful. The psychological reason ties in to this predisposition. With the obvious exception of sociopaths (those who feel no empathy towards other people), most people feel positively terrible when they kill someone—even for legitimate reasons, like self-defense or in a battle field (or stoning an unruly child). It is so impactful, in fact, that there are reports of physical manifestations of these feelings of guilt, such as panic attacks, vomiting, crying, and even PTSD (which, I suppose doesn’t really count as “physical”, but you get the point).