The Ontology Of God
there's at least a general sense by which the concept [God] can be understood.I'm not entirely sure I would be willing to concede this to the theist. In terms of the ontology of God we are never offered any positive or primary ontic properties, only relational or negative properties. I don't believe it's possible to discuss anything without positive/primary properties, (nor would we accept this in everyday situations) and hence we still don't know what God is. [1,2]
and strong agnostics who take such an entity as being unknowableAs an aside: isn't identifying God as "being unknowable" a truth claim?!
Logical Problem of Evil
When it comes to the conception of God as being omnipotent, omniscient, and omnibenevolent, the existence of such a concept is seen to be incompatible with the existence of evil. Such a conception of God can be ruled out, and indeed much time and effort has gone into addressing this concern. The problem of evil is justification for being a strong atheist, at least in respect to conceptions of God that involved absolute power and absolute goodness.This is known as the logical problem of evil and it doesn't seem stand up in it's strongest form. Theists may be justified in their belief that all appearance of evil has a rational explanation (known as Skeptical Theism) that we may only understand if we too knew everything. We don't know everything therefore there might be good reasons for evil or apparent evil to exist.
A weaker form of this argument is to state that the level and amount of suffering makes much more sense under atheism than theism (argument to the best explanation) and the theist needs to demonstrate why evil can serve some greater purpose.  This is generally a good rhetorical trick because it makes otherwise intelligent Christians justify genocide, etc. 
The Ontology Of God
Likewise other traits are problematic.I think the strongest is the impossibility of omniscience (it's impossible to know everything).  There is also the problem of omnipotence, being all-good and being free. If God can do everything and is free to do anything than that includes being evil. But it is metaphysically impossible for God to be evil. Also, as humans can be evil but God cannot - it stands to reason that we can do things God cannot. Hence he cannot be omnipotent. 
God vs Logic
can God make a rock so heavy that he can't lift?An objection to this is to note that such a sentence is logically meaningless and hence the theist can modify the definition of omnipotent to mean "that whatever is logically possible". Such a concession may make some theists uncomfortable as it means that God is inferior to logic! If they do not concede this then logic is arbitrary and/or God is above/beyond logic and is therefore meaningless for humans to pontificate over.
Deductive vs Inductive Approaches
These kind of proofs though are at least to me unsatisfying because while they ground God in definition they don't capture the essence of what God is.There are two ways to arrive at God. One is through pure reason (Anslem, Thomas, Scholastics), the other is through evidence (Natural Theology). Pure reason lead us to abominations such as the ontological argument for God! It's also a shaky edifice because to undermine any conclusion makes it almost impossible to patch one's argument. On the other hand natural theology sounds more like what the average person identifies with as God.
Boundaries/Scope of Explanatory Power
Can something supernatural act within the natural world?I don't see how this is metaphysically impossible. I like to think of it this way - imagine we are in the matrix and those outside the matrix are "supernatural". Although those inside the matrix cannot interact with the matrix (unless there are built-in mechanisms), those on the outside can affect things inside the matrix.
If something is acting in the natural world what stops it being natural itself?Supernaturalism has generally meant something along the lines of acausal will generating actions (i.e. uncaused causes, contra-causal free will, etc)
Can something simultaneously be in and outside of time? Can something outside of time experience or be said to have a thought?There are serious coherency problems here in that humans, who are beings in-time, find it hard (if not impossible) to talk about these things. I try to stay away from it!
An undetected and undetectable deity is indistinguishable from there being no deity at all.It's actually much worse than that! Even if there was some miracle, it is epistemically equivalent to highly advanced technology. It's impossible to tell the difference between a booming voice from the sky and aliens messing with us. 
Altering the brain alters conscious experience.Have you heard of the split-brain patient where one half of his brain is an atheist and the other is a Christian? 
Tea Pot Skepticism
Nor could they disprove Santa for that matter, or an alleged china teapot orbiting between Earth and Mars too small to be detected by any instrument.I'd be wary of taking this line of thinking too far just as a matter of principle - we don't just disbelieve these claims (Santa, tea-pot's) on the absence of evidence alone but because there are also good reasons to suppose they are not true.
First Cause Arguments
the notion of a clockwork universe, with notions like the arrow of time and causality probabilistic rather than definiteThis one is a bit tricky depending on which QM interpretation you follow - there are currently at least 12.  In terms of the Kalam Cosmological Argument - it's foremost Christian proponent William Lane Craig says that it only works under A-theory of time (that time has a direction, etc) instead of B-theory of time (time is a 4D unchanging manifold). Despite Craig's defense of A-theory, many philosophers remain unconvinced over A or B (it's one of the most uncertain areas of philosophy) and the jury is still out.  Physicists would likely be more comfortable with B-theory. For example, in Hawking's new book  he advocates something which resembles B-theory. Not all A theorists are theists - you could still argue against Kalam with A-theory. 
There's no reason to assume that life, and more specifically us, is the focal point for the laws of physics. Evolutionarily so much owed to our existence is a product of contingency that it makes no sense to privilege us more than any other life-form.Two problems with this. If there is only one universe then the existence of humans seems extremely improbable and very surprising.  Secondly evolutionary contingency can only exist when life is able to start existing - hence stars need to last a certain amount of time, the universe has to be a certain age, etc. While I could write for pages and pages about good ways to handle the fine tuning argument I can actually just point to Christian philosophers who actually argued that our "fine tuned" universe is equivalent to a "coarse tuned" universe if we do not have a probability distribution on what values the constants could have. 
Morality, evidentially, clearly is an evolved trait and requires no further explanation.I recently debated a fellow atheist in our atheist club at university over the existence and nature of morality. My position is basically that objective morality doesn't exist (moral skepticism/nihilism) but that moral behaviour certainly does exist and must be evolutionary. I would say its very difficult if not impossible to get from moral behaviour to absolute morality without presupposing a miracle! (Then there is the issue of how the describe the ontology of absolute morality in a naturalistic framework. )
Cognitive Basis for Religion
We are wired for agency and in particular human agency.Worse still we are wired to remember minimally counterintuitive ideas. Almost all supernatural entities can be reduced to singular ontological violations. Ghosts = People - Body's, Zombies = People - Soul, Magic Pendant = Object + Ability to listen, etc [16, 17]
In this respect, explaining God belief is just one of the many weird things that permeates in our species without good reason.Our brains are still basically the same since when we left the Savannah some 100,000 years ago. We have stone age brains in a modern world with atomic weapons/global warming. This should alarm anyone! Even if you take God belief away, it transforms into New Age or any other metaphysical/existential crutch.
I find the quest for justifying belief to be difficult. At what point do you stop researching and just get on with your life? For most weak atheists it's just about simply pointing out that the traditional theistic arguments don't resonate with them and until they do, one is justified in not accepting them. Perhaps its just a case of doing what one usually does in cases where expertise is required - and that is to tentatively appeal to the authorities? So long as there is a vanguard of intelligent and sophisticated atheist philosophers of religion, we need not fear the development of some new fangeled attempt by Christian philosophers to bamboozle us into accepting some seductive sounding ontological argument.
All I know is that I learn the most when I push my atheistic brethren and see where it goes.
 George Smith "The Case Against God"
 Youtube, ProfMTH "What is God?"
 William Rowe "The Evidential Argument from Evil"
 William Lane Craig, "Slaughter of the Cannanites"
 Problems with Devine Omniscience
 For these and others (apparently there are PLENTY of incompatible properties of God), see Michael Martin.
 Gregory Dawes "Theism and Explanation"
 V.S. Ramachandran
 Interpretations of QM
 Stanford Encyclopedia of Philosophy on Time
 Hawking, "The Grand Design"
 Quentin Smith (I think...)
 Luke Barnes presents a terrific introduction to this.
 Lydia/Timothy McGrew
 J.L. Mackie (Argument from Queerness)
 Pascal Boyer "Religion Explained"
 Scott Atran "In God's We Trust"