There is another problem, this one less important. Reichenbach says:
Although Aquinas was quick to make the identification between God and the first mover or first cause, such identification goes beyond the causal reasoning that informs the argument. Instead it requires a lengthy discussion of the supreme beings that are found in the diverse religions and careful correlation of the properties of a necessary being with those of a religious being like God, to discern compatibilities and incompatibilities (Attfield).
This is often said; but it has never made any sense to me as a complaint against Aquinas. Aquinas is actually very careful and reasonable on this point. The usual point of an argument for the existence of God is that you argue for something that at least some people have traditionally called 'divine' or 'God' or somesuch. Or else, failing that, you argue for the existence of something having a description someone could reasonably consider to be a divine attribute. 'God' is not a proper name; it is a common noun that is treated as a proper name because people (even atheists) have gotten used to the idea of its applying to only one actual thing. If by 'God' you mean the one actual thing to which this description would refer if Christianity is right, then the cosmological arguments don't conclude to the existence of God in that way; they only do so under limited types of description. Nor would it be reasonable to expect otherwise. I cannot fault an argument, designed to show the existence of the Prime Minister of Canada, on the basis that the argument doesn't conclude 'This particular man, Paul Martin, with all these particular sorts of properties, exists' but only 'There is a Prime Minister of Canada'. The latter is all you need from the existence argument. If you are interested in other things, then you take the existence argument and use it to move on and look at other things. And this is precisely what Aquinas does; nor is he "quick" to do it, unless you think the entire Treatise on God in the Summa Theologiae or the entire first book of Summa Contra Gentiles can be called "quick" discussions. The existence arguments only yield something(s) with properties that can reasonably be called 'divine'; that's all he actually needs in the argument itself, and that's all he asks we recognize - because he can use these properties to deduce other properties and start filling out the details of what you actually can know about this 'God' you've shown to exist. And this is exactly what one would expect. But, as I said, this is a relatively minor beef; it only affects Aquinas.
My real complaint about the article (it is not alone) is that it spends way too much time on Craig's Kalam argument and nowhere near enough time on the traditional arguments, which get massively shortchanged. This is unfortunate, because actual objections relevant to the traditional (especially medieval) arguments are hard to find - all three of the people from whom the main objections to the traditional arguments tend to be taken (Russell, Hume, and Kant) can fairly easily be shown not to have had any considerable acquaintance with the traditional arguments; and it's unclear how any of the three objections Reichenbach gives actually are relevant to (say) Aquinas's or Scotus's arguments, since those arguments are arguments to the effect that, if you allow that there are certain properties that are caused, to deny there is a first in each of these causal series leads to contradictions. And they actually have arguments for such a conclusion (sometimes in other places). The vague handwavings of Hume, Kant, and Russell do nothing in comparison with that, even on the assumption that they are more-or-less right.
I don't want to give the impression that it's a bad article. It's actually quite good, well worth reading, particularly given how condensed it has to be as an encyclopedia article. The fact is, 'cosmological arguments' is an immense and complicated subject whose surface can barely be scratched by a discussion this short. I would say: it's a good place for people to start. And that's exactly what an encyclopedia article should be.
(My attention was called to this entry by a post by Matthew Mullins at Prosblogion.)